Barbara Bush Reveals Daughter Spent Time in NICU Named After Her Grandmother: 'It Felt Divine'

Barbara Pierce Bush expected to welcome her first baby with husband Craig Coyne in New York, but Cora Georgia had her own plans.

The baby girl arrived "almost six weeks early" during their visit to Maine — an event made even more special because Cora stayed at the neonatal intensive care unit (NICU) at a hospital in Portland named after Barbara's late grandmother, former First Lady Barbara Bush, who passed away in 2018.

"It's been incredible. It's been better than I even thought it would be," Barbara tells PEOPLE about welcoming her daughter during a joint interview with her twin sister Jenna Bush Hager, while promoting their upcoming children's book. The Superpower Sisterhood will be published by Little, Brown Books for Young Readers on April 19.

Barbara says that what made the experience "incredibly meaningful" was visiting Cora in the Barbara Bush Children's Hospital. She says she and her husband "had no idea" that the NICU was named after her late namesake.

"I went there to go visit her and looked over on the wall, and it said Barbara Bush Children's Hospital," Barbara, 40, remembers. "So, in many ways, it felt divine that she was born in Maine near where we were married and where we have so many memories as a family. Then I felt how poignant and meaningful it was in a place that meant something to my grandmother."

Since baby Cora was born premature, she ended up staying in the NICU for about four weeks, her mom says. "She was premature and very healthy," says Barbara. "She just needed some help figuring out the basics like breathing and getting stronger to be able to do those things on her own."

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Barbara and Coyne didn't expect to meet Cora so soon — aunt Jenna had to make a last-minute Target run to get diapers and a car seat, Barbara recalls — but they couldn't be happier with their baby girl.

"It's incredibly natural and shocking how easily she fits into our life, even though we have never met her seven months ago," says Barbara, who explains they were able to spend the month of January with her parents, former President George W. Bush and former First Lady Laura Bush, before moving back home. "So it's been a lot of learning, and it's been a huge joy for me."

Now 6 months old, Cora is a "cute chunky little babe," Barbara says. Coyne is a "wonderful dad" and they take Cora everywhere with them. For Barbara, every moment with her daughter is special.

"On her six-month birthday, two little bottom teeth popped through, which was very cute," she says. "But I think my favorite milestones are of her smiling, going in the morning to wake her up, and her giggling... She is incredibly joyful."

Before Cora was born, Barbara wrote The Superpower Sisterhood with her daughter in mind. She and Jenna reference their three girls in a joint dedication in the book. (Jenna shares daughters Mila, 8, and Poppy, 6, and son Hal, 2, with husband Henry Hager.)

"To our daughters — may you use your powers to empower others," they wrote.

Barbara, the CEO and co-founder of Global Health Corps, and Jenna, the co-host of Today with Hoda & Jenna, were inspired to write their latest kids' book during the book tour for their bestseller, Sisters First.

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"There were so many people that said, 'Gosh, I wish I had a sister, like you and Barbara [have],' " Jenna says. "It reminded us a lot of our mom, who was an only child, and that sisterhood comes in so many different ways."

The result is The Superpower Sisterhood, which follows a young girl named Emma, who wants more kids to play with. When two sets of sisters move to her street, they quickly become friends and realize their unique talents are even more powerful when they support each other.

Barbara explains that the book is "is a love letter to sisterhood" in all of its forms. She wants Cora to have an equally powerful support system as she grows up.

"What we're trying to show is each of the girls are great at something different. And we can each be unique in our own way," she says. "When we have friends that are great or interested in other things, that opens up our lives as well. So, when [my daughter is] older, I hope she emulates that with her friends."