Ms. Williams and her sister, though, had other issues to resolve. Ms. Williams, who has a lesbian partner, had a biological child, Jamison, 6, who was conceived through a sperm donor, too. And the sisters wondered how to describe the relationship between Mallory and Jamison, who are not only biological half-siblings, but also cousins. And where did the sperm donors fit in?

After months of discussion, they came to a resolution: “Mallory is my daughter and Jennifer is her aunt,” said Ms. Ashmore, 38, who lives close to her sister near Minneapolis. At home, Jamison sometimes refers to Mallory as his sister. But at school, said Ms. Williams, 40, “she’s his cousin.” The sperm donors, they agreed, had no place on the family tree.

For some children, having to explain their family tree can be alienating.

“It can cause kids pain in unexpected ways,” said Peggy Gillespie, a founder of Family Diversity Projects, a family education advisory group.

At Green Acres last year, Ms. Murphy said, two kindergartners were playing outside when a boy, the son of a single mother, told a classmate that he had an older sister. “You can’t have an older sister; you don’t have a dad,” Ms. Murphy recalled the girl saying. The boy protested; he said he knew his sperm donor, who had a daughter of his own.

Sue Stuever Battel and Bob Battel of Cass City, Mich., will soon have four children. The oldest, Addy, 8, was conceived naturally; Dori, 5, was conceived via a sperm donor. They are adopting two toddler boys. “All four of our kids are 100 percent in our family tree,” Ms. Battel said. “The genetic connection has never mattered.”

But the Battels understand that their children may have questions. So they have prepared two sets of baby books: one outlining life with the Battels, the other about each child’s birth parents. The children can choose which details they want to share.

Ms. Battel and her husband also debated whether to include other children born using their donor’s sperm. After all, those children would be biological half-siblings to Dori. Their verdict: “We decided they are not half-siblings, but donor siblings,” Ms. Battel said. “We honor them, but they are not part of the family.”