"I called my mom and said now is the time! We need to write this book," Jenna tells PEOPLE.
The book, inspired by the Bush family's love of exploring nature, tells the story of a little girl named Jane who takes a summer road trip with her family to visit national parks around the country. The former First Daughter says she wrote most of the book and let her mom handle the editing.
"Jenna and I wanted to write another book, and had been discussing one for years," Laura explains to PEOPLE. "I hike in the national parks every year with my childhood friends, and encouraged my girls to love the outdoors … And in some ways it is a sequel to Read All About It (the mother-daughter duo's first children's book) so it was easy and fun to write."
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Our Great Big Backyard, due out in May to commemorate the Centennial Anniversary of the National Park Service, has already won the approval of two very "discerning customers," says Jenna – her daughters, Mila, 2, and Poppy.
"We have read it to them … and they loved it! The little girl, Jane, has an active, creative imagination that reminds me of Mila's."
The Today show correspondent, who lives with her daughters and husband Henry Hager in New York City, says her girls "love to be outside" so they often play together in the city parks. But nothing beats the view at the Bush family ranch in Texas. "We recently took them both to Texas to spend time with their Grammy and Jefe (Jenna's dad, former President George W. Bush) on our ranch. On our first night as we walked Mila to bed, she looked up and in disbelief said, 'Moon!' I think she thought the moon was something that only existed in books."
Source: Jenna Bush Hager / Instagram
Marveling at the bond her two granddaughters already share, Laura adds, "Mila thinks Poppy is amazing! And little sisters Mila and Poppy remind me of little sisters Jenna and Barbara (Jenna's twin sister). They all love stories and they love to read books. I am happy that Mila and Poppy have each other, just like Barbara and Jenna do."
Bush fans can look forward to plenty of fun family insider jokes sprinkled throughout Our Great Big Backyard.
"We asked our illustrator, Jacqueline Rogers, to draw Baxter the dog to look just like my first dog, Bully," says Laura. "I even showed her a photo of Bully and me when I was a little girl. But Baxter was the name of one of our favorite cats."
"The whole story is based on the most precious memories of my childhood, which all took place outside with my family," adds Jenna.