In many ways, Ms. Schwarzenegger Pratt has created a version of her own childhood for her daughters. Like her mother, she has built a career as an author and media personality, and also married a famous actor. She lives minutes from where she grew up and regularly visits both parents, who separated in 2011 and finalized their divorce in 2021. Ms. Shriver hosts a weekly mommy-and-me class for Lyla and her friends, and Mr. Schwarzenegger keeps a miniature pony in his backyard that the girls love to pet.

Ms. Schwarzenegger Pratt said she would not change anything about her childhood. “I know this sounds crazy, but I really would love to just do exactly what they did,” she said of her parents. “I look back on how much of life my parents kept private, and I have a lot of respect for it. I think they kept a lot of their relationship private, they kept us kids private — you know, they didn’t take us to red carpets, they didn’t have us parading around in front of everybody.”

Now What?

Ms. Schwarzenegger Pratt may have had a relatively private childhood, but once she got to college, she wasted no time starting a public-facing career. She landed her first book deal at the age of 19, when she was a sophomore at the Annenberg School for Communication and Journalism at the University of Southern California. That book, “Rock What You’ve Got: Secrets to Loving Your Inner and Outer Beauty from Someone Who’s Been There and Back,” was inspired by a summer she spent interning at a P.R. company that handled Dove’s “Real Beauty” campaign. It became a New York Times best seller, and Ms. Schwarzenegger Pratt went on to publish two more nonfiction books for adults — “I Just Graduated, Now What?” in 2014 and “The Gift of Forgiveness” in 2020 — as well as a children’s book, “Maverick & Me,” inspired by her rescue dog, in 2017.

A few months after Lyla was born, she also began hosting a weekly interview series on Instagram, where she has one million followers. The show is called “B.D.A. Baby” — that’s “before, during and after baby” — and on it she talks to other celebrities and experts about pregnancy and parenting, tackling questions that have come up in her own life. “Like, ‘OK, I’m introducing solids, like how are we doing that?” she said. “Or I’m pregnant again, what’s that going to be like?’”

Ms. Schwarzenegger Pratt tends to pick projects based on whatever she is going through at the time, she said. She wrote “I Just Graduated, Now What?” for example, when she was trying to figure out what to do with her career after graduation. Her work is personal, then, but not particularly revealing. On “B.D.A. Baby,” she lets her guests do most of the sharing, and in her books, she avoids making any disclosures that could end up in the tabloids. She mentions her parents’ divorce only once, obliquely, in “I Just Graduated,” noting that she moved in with her mother after college to be closer to her after the separation.