Photo: Courtesy Amber Thibault

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Amber Thibault and Floyd “Ray” Cosgrove were thrilled last year when they found out Thibault was pregnant with their second child. But they never expected that their lives would be turned upside down the day she was born.

“[Doctors] didn’t know what it was at first,” Thibault, of Redding, California, tells PEOPLE. “They told me she had really low-set ears and that her head was cone-shaped. They started feeling around and realized it was her skull. Then they said they were pretty sure it’s Pfeiffer syndrome.”

Pfeiffer syndrome is a rare, genetic disorder in which some skull bones fuse together and grow abnormally,according to the National Institute of Health. The growth usually leaves children with high foreheads, wide-set eyes, an underdeveloped jaw and an altered nose. The illness affects one in 100,000 people, the NIH reported.

Courtesy Amber Thibault

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Thibault, 27, says the condition is so rare that doctors never thought to check for any signs during her pregnancy. She was “in shock” when they receieved the diagnosis.

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Still, the mom had to come to terms with her daughter’s syndrome. And Thibault says she cried in her hospital bed as she researched Pfeiffer online — and learned that the late singer,Prince‘s,son had the syndrome and lived for just six days.

“Her surgeon told us that as long as [children] get the surgeries and procedures that they need on time, they should have a normal life expectancy,” Thibault says. “That made me really excited. I was so scared every night that I’d wake up and she wouldn’t be here anymore, so that just made our day.”

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When Halle was five weeks old, she underwent a dangerous surgery in which her skull was removed to reduce swelling. Now five months old, she’ll need to undergo several more surgeries in the future “to make room for her brain.” She will undergo Chiari decompression surgery in November, which doctors say will help with any speech delays and sleep apnea.

Despite the invasive surgeries, Thibault says the family has been adjusting well to life with Halle.

“We thought it would be a huge struggle, but I think it’s brought our family closer together,” Thibault tells PEOPLE, noting that her toddler son Sawyer loves being a big brother. “He loves her. He’s constantly trying to pick her up out of her swing. He loves having a sister.

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“When she grows up, people with disabilities are always gonna have some insecurities,” she tells PEOPLE. “I want her to know that I think she’s beautiful and I’m not afraid to show her off.”

source: people.com