Inside Meghan Markle's Ultra-Private Birth Plan: 'They Could Enjoy the Birth in Peace,' Says Source

“Meghan and Harry are both very thankful for how smoothly things went,” a source tells PEOPLE

On June 4, Meghan Markle welcomed her baby girl, Lilibet Diana, at Santa Barbara Cottage Hospital, a short drive from Meghan and Prince Harry's Montecito, California, home.

"They looked at several hospitals before they settled on the Santa Barbara Cottage Hospital," a source tells PEOPLE in this week's issue. "Meghan loves that it's female-founded."

Meghan's care was overseen by Dr. Melissa Drake, with remote support from Dr. Gowri Motha in the U.K., who helped oversee the care during the birth of Archie at London's Portland Hospital.

The facility's state-of-the-art childbirth center offers a family-centered, individualized approach to birth. (In addition to a menu to order room service and a comfy sofa for Harry!)

Santa Barbara Cottage Hospita. Google Maps

"Security and privacy were also priorities," the source adds. "They had a big security team that the hospital needed to accommodate."

Prince Harry and Meghan Markle. Karwai Tang/WireImage

In March, the couple spoke to Oprah Winfrey about the stress of introducing their son Archie to the world just days after his 2019 birth in the U.K.; this time Meghan was able to quietly deliver the baby two days before sharing the news, with no pressure for a public press conference.

"Meghan and Harry are both very thankful for how smoothly things went," the source adds. "They could enjoy the birth in peace."

Meghan Markle and Prince Harry with son Archie in 2019. DOMINIC LIPINSKI/AFP via Getty Images

In keeping with the 20-week paid parental leave policy of their Archewell Foundation, both Meghan and Harry plan to take several months off to spend time with their daughter, Lili.

Still, their ongoing projects remain in high gear, including an upcoming docuseries for Netflix on Harry's Invictus Games and the release of Meghan's first children's book, The Bench, which was inspired by a Father's Day poem she wrote for Harry after they welcomed Archie ("the man and the boy who make my heart go pump-pump," as she writes in the book's dedication).

Meghan Markle and Prince Harry. Karwai Tang/WireImage

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But as they embrace their new status as a family of four, they plan to concentrate on life at home for a while.

"Meghan and Harry are taking time off to focus on their family," the source adds. "They want to have a long summer break together as a family."