And she had to make some judgment calls about what she found out.

Her findings were organized in a book, which Maude noted was intentionally printed on only one side of the page, to allow “plenty of room for future generations to continue the records.”

Ms. Davis took up the challenge. Once she embraced the hobby of genealogy, as well as the unofficial title of family historian, she enjoyed advantages Maude lacked, including internet searches from a home computer and ubiquitous DNA testing.

Like her great-grandmother before her, Ms. Davis also had to make judgment calls of her own, weighing affection for her family against her duty to render an accurate account for future generations. The hardest one involved crucial information she discovered that wasn’t in Maude’s family record.

Many families boast a member who is the keeper of pictures, documents, memories and the family tree. As DNA testing spreads—there are now millions of family trees online—that job is confounding and frequently unsettling.

Along the way, Ms. Davis, who is 53 years old, asked herself, “Do I want to know all this?”

In previous eras, people compiled histories to learn about their heritage or used the family tree to bolster social status. Resulting accounts were often a mixture of useful information and stories “that need to be taken with a grain of salt,” said Terry Koch-Bostic, chair of education at the National Genealogical Society, a nonprofit based in Falls Church, Va.

DNA tests challenge all that. Family genealogists must now juggle the privacy of their relatives, some of whom don’t want to be involved, alongside the curiosity of strangers who arrive with evidence that they are part of the family and may want to establish a relationship.

“What do you owe these people?” said Steven Mintz, a professor at the University of Texas at Austin who specializes in the history of families.

Hoping to find new clues, Ms. Davis bought DNA tests for her parents in 2013. As soon as she got the results, “the family tree on my father’s side exploded,” she recalled.

DNA results helped lead her to a relative who accused a neighbor of hexing his cows during the 17th-century Salem Witch Trials. (The neighbor was hanged.) She was excited to find at least six kinsmen who fought in the American Revolution. Millard Fillmore, 13th president of the U.S., was a distant cousin.

Testing also turned up unexpected modern relatives.

After Ms. Davis’s parents took DNA tests, she was excited by dozens of requests for contact from people who apparently shared a common ancestor. Ancestry, the company Ms. Davis used, allows members to send messages to one another within its site.

She spent hours working with newcomers to help them figure out where they fit on her genealogical charts—and in the lives of her family. Many, she found, were curious about their roots, and nothing more.

One genetic match, a cousin, told Ms. Davis he hadn’t known his father but was told he had Irish and Puerto Rican roots. She saw that both he and her father were descended from someone who emigrated in fact from neither place, but from Kilmarnock, Scotland, in the early 1900s.

When members of her extended family reached out to the new cousin, though, he asked her to spread the word that he wasn’t interested.

“I can respect that,” she said. “He got what he needed. He wasn’t interested in establishing all these relationships.”

Another time, Ms. Davis contacted a woman she didn’t know who showed up on a list of genetic matches. The woman’s father—a distant relative—had been adopted and the woman was curious about his ancestry. Ms. Davis sent her a note, welcoming her to their family. “Thank you, I have a family,” the woman replied. She wanted information only about her heritage.

Once news of DNA test results spread within her extended family, Ms. Davis said relatives started sharing all kinds of stories, some of which surprised her. Being a family historian involved acting as “the mediator, the strategist, the psychologist,” she said.

The main family historian, Viola Maude Robinson, known as Maude, died in 1995 at the age of 97. She had five children who lived to adulthood. One was Ms. Davis’s grandmother, Eva. The other four, all boys, Ms. Davis describes as gregarious, charismatic and “known for their adventures.”

Last year, while making one of her regular checks on the DNA testing account, Ms. Davis saw a new match, someone listed as a likely first cousin to her father. If confirmed, that meant the woman, named Kit Pull, was also a grandchild of Maude.

The news made Ms. Davis uncomfortable. Ms. Pull’s father would have to be one of Maude’s four sons, who had a total of 17 children from their marriages.

She sent a message to Ms. Pull to see if she was interested in learning more about the connection.

Ms. Pull replied right away. “I am adopted and know almost nothing about my family history,” she wrote. “I would be very interested in comparing information with you.”

She wanted to know the identity of her biological father. She was eager to meet any new half siblings. These would be people Ms. Davis grew up with and loved. She just didn’t know which ones yet.

Ms. Davis was sympathetic to Ms. Pull’s desire to know her genetic origins. But the discovery was going to change the life of other family members too, and they didn’t have much say in the matter.

She worried her family would be upset with her. “I don’t want anyone feeling I betrayed them.”

Ms. Pull talked on the phone with Ms. Davis’s father, Ron Smith, who said he felt warmly toward her. “She seems like a pretty good person,” he said. He agreed Ms. Pull’s quest might shock his cousins, but also understood the intense desire to know one’s identity and history.

“All these people are human beings,” he said. He was hopeful that any possible upset might wear off over time.

So on an afternoon in April, Ms. Davis agreed to meet Ms. Pull at the library in Hastings, Mich., the town where Maude grew up. They would go over Ms. Pull’s DNA results and try to figure out which of Maude’s four sons, all of whom are deceased, was her father.

Maude compiled the family history in books and sent copies to 25 children and grandchildren. She donated copies of the blue-bound hardcover books to the library in Hastings and the Michigan History Center.

When Ms. Pull, who is 67, arrived, she ran across the street and gave Ms. Davis a hug. The women headed inside the library.

Ms. Pull had been adopted when she was seven days old. She described a happy childhood, adored and spoiled by her parents. She celebrated two birthdays. On the day she was born, her parents gave her birthday presents. On the day she was adopted, the family went out for dinner. “It was always a special thing,” she said.

In 1968, when she was 16, she got pregnant. Her parents sent her to a home for unwed mothers. “They told people I had gone away to school for a while,” Ms. Pull said. She gave birth to a daughter, who was also adopted.

In 1991, when she was 39, Ms. Pull got a call from a person who said she had been asked by Ms. Pull’s biological daughter to track her down. The young woman wanted to know her family health history. When Ms. Pull called her biological daughter she told her, “I was adopted too. I know nothing about my background.”

Ms. Pull, who raised two other children, wanted to help nonetheless. She asked the intermediary to help find her own biological mother. She hoped to get answers. But when they located Ms. Pull’s biological mother, she refused to accept her letter.

She was devastated. “I felt like I was a skeleton in her closet,” she said. Ms. Pull said her adopted parents had never been given the name of her biological father and she didn’t have the heart to continue a search. Ms. Pull and her biological daughter keep up from time to time.

In 2017, Ms. Pull’s husband bought her a DNA kit for Christmas. She spat into a tube, and sent it in. When she got her results back, she saw a list of genetic matches, along with how much DNA she shared with them.

Siblings share around half their DNA. Half siblings share a quarter; and first cousins, on average, share 12.5%. Based on the numbers, Ms. Pull and Ms. Davis’s father appeared to be first cousins. “I realized I had another family out there,” she said.

Now she and Ms. Davis sat side by side, sharing a computer at the library, to go over the DNA results together.

Both women had initially assumed Ms. Pull’s father was a son named Arnold, the only one of the four brothers who had done DNA testing, because he showed up as one of her highest genetic matches.

Now that Ms. Davis was able to see the amount of common DNA, she realized Arnold and Ms. Pull didn’t share enough to be father and child. He was her uncle.

Children of two of Maude’s other sons had also done DNA testing. They were genetic matches for Ms. Pull, but the results indicated they were her first cousins, not her half siblings.

“It hit me at the same time as it hit Kit,” said Ms. Davis. There was only one brother left.

Richard was Maude’s oldest son, a decorated World War II hero. In 1942, pinned down with his unit during the Battle of Guadalcanal, he came under enemy fire, taking shrapnel in the chest. In the confusion of wartime, the Marines sent Maude a letter informing her Richard had been mortally wounded. Maude collapsed in shock.

Three weeks later, Maude received a letter from Richard and learned he was alive and recovering in a military hospital. He later received the Purple Heart.

Ms. Davis took out her own copy of Maude’s book, and showed Ms. Pull a picture of a young man in a sharp military uniform.

“This is my father,” Ms. Pull said, her voice filled with wonder. “Welcome to the family,” Ms. Davis told her. Ms. Pull started to cry.

Of the four brothers, Richard was considered a straight arrow. He worked in a factory in Lansing then returned home in the evening to more responsibilities on the family farm. He doled out advice and help to the extended family. He and his wife, both deceased, were married almost 52 years. Richard’s wife cared for both Richard and his mother, Maude, during their final illnesses.

The women did a quick calculation; Ms. Pull was born less than a year after the youngest of Richard’s four children.

“Do you think my siblings will accept me?” Ms. Pull asked.

Ms. Davis said it would be a shock to them, but, nonetheless, promised to reach out to Richard’s daughter, Rebecca, with whom she was closest, to share the news.

After Ms. Pull left, Ms. Davis stopped at the local cemetery to visit Maude’s grave, pulling out weeds that had grown around the headstone. She was happy for Ms. Pull, but nervous about what lay ahead.

In May, she told Richard’s daughter, who is 71, about the DNA test results. Ms. Davis asked her whether she would take a DNA test to confirm the suspicions that her father was also Ms. Pull’s father.

“She said, ‘Oh,’ then didn’t say anything,” Ms. Davis recalls. “That was the moment my heart started to hurt.”

She told her cousin, “I am sorry my doing genealogy has opened up Pandora’s box.”

A week later, she contacted her again. Rebecca had decided to take the test.

In June, Ms. Davis got a text at 6 a.m. from Rebecca. The results were back. They got on a call and went over the numbers.

Based on the amount of shared DNA, Rebecca and Ms. Pull were indeed half sisters. Ms. Davis said Rebecca thanked her, then ended the conversation.

Ms. Pull checked her Ancestry account page. After weeks of waiting, she saw Rebecca’s name on the list of her genetic matches. “There is a lump in my throat,” she said later that day. She had her confirmation.

Ms. Davis and Ms. Pull couldn’t figure out how Richard might have met Ms. Pull’s mother. At the time Ms. Pull was born, her mother was unmarried and 33 years old. Richard would have been 29, busy raising four young children.

Ms. Pull knew from her biological mother’s obituary that she had worked in a state government office in Lansing, Mich. Richard worked in a factory in a different part of the city. Ms. Davis’s father pointed out that a number of people in Richard’s family were employed in state government offices. Maybe Richard had given a family member a ride to or from work and bumped into Ms. Pull’s mother. Perhaps they met at a restaurant in town.

“The answer is probably lost to history,” Ms. Davis said.

The repercussions weren’t. Ms. Davis found herself navigating new territory, as the intermediary. During one conversation, Rebecca asked, What does Kit want?

“I don’t really know,” she replied.

Ms. Pull asked her to pass along this message: “I want to know if any of my brothers and sisters are interested in developing a relationship with me.”

Then she apologized. “I’m sorry you’re in the middle of all this and you have to be my back and forth,” she told Ms. Davis. “I love you.”

Despite Ms. Davis’s efforts to give her cousins space, word about Ms. Pull reached other family members. A distant cousin who did DNA testing saw her name on her list of matches and wanted to get in touch. Ms. Davis suggested holding off a while. She struggled to balance the warmth of some family members eager to embrace a new relative, with the desire to give Rebecca and her siblings time to sort through their feelings.

Recently, Ms. Davis drove her father to Ms. Pull’s house so the first cousins could meet. She wanted her to know that, no matter what happens, “Kit has found family with me and my dad.”

Ms. Pull appreciated the gesture. She has started gathering material to make a scrapbook of her own about her biological father that she could someday give to her children. She still holds out hope of one day being part of the record Maude began.

“If I am going to be part of the family,” she said, “I want to be included in the family history.”

When it came to genealogy, Ms. Davis considered herself Maude’s heir, solving historical puzzles to add to the blank pages in her great-grandmother’s book. She assumed Maude presented all the information she found about the sprawling family.

Then a few years ago, while doing her own research, Ms. Davis discovered spots in the book where Maude’s record was incomplete.

In one case, one of Maude’s other sons had a child with another woman the same year his wife gave birth. In the blue book, Maude moved the birth date of the other woman’s child to a different year. Ms. Davis thinks Maude didn’t want people to know both women were pregnant at the same time.

Ms. Davis had always felt that people’s foibles and challenges made them relatable and should remain part of the official record. After her own recent experiences, she saw Maude’s choices in a new light.

“I might be a little bit more like Maude than I thought,” she said.

Write to Amy Dockser Marcus at amy.marcus@wsj.com