Shawn Johnson East tells PEOPLE she experienced "very low moments in those first couple of weeks" after bringing home her second baby, son Jett James

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Adjusting to life as a mom of two was no easy transition for Shawn Johnson East.

The Olympic gold medalist welcomed her second baby, son Jett James, with husband Andrew East on July 19, expanding her family that also consists of daughter Drew Hazel, who turns 2 next month. As she tells PEOPLE, navigating newborn duties with a toddler in the picture was a rocky road at first, but now they've found a rhythm amid the "absolute chaos" at their house.

"I've had massive meltdowns," Johnson East, 29, says during a conversation surrounding Philips Avent's new line of baby products. "My biggest fear in having a second kid was Drew was my baby, she was my everything. And just like before having her, I couldn't picture having another human sharing my heart and sharing my life."

"When I came home, the transition was really hard, because instead of having her there and being able to be like, 'It's okay, baby, you're still my baby, but we have another baby,' she was sick and she had to go stay with Grandma and Grandpa," she recalls.

"I had some very, very low moments in those first couple of weeks, just because I missed my baby girl and I wanted to make sure she knew she was loved," the former gymnast adds. "It's just that rough transition of splitting your heart and sharing it, and trying to show your love to your babies equally."

She says, "We've worked really hard to make sure she feels loved."

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The star did find herself more confident with baby No. 2, having already gone through the new-mom crash course of caring for a newborn almost two years ago. She again relied on Philips Avent's baby products this time around, as well.

"I partnered with Avent back with my daughter, back when I knew absolutely nothing about being a parent. I was like, 'Well, these are cool products,' but I didn't have a kid at the time. Then I had my daughter and every Avent product was her staple," she says. "And that's not an exaggeration — their products are literally my lifeline."

"With my daughter, over time I learned what products work, but I didn't know why. Now, having the confidence and going through everything, with my son I know why products work," continues Johnson East. "There's science and actually strategy behind it. It's why all their stuff works."

She adds, "I think now, as a mom of two with Jett, I just felt so much more confident."

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Johnson East says Drew is "definitely getting into that phase where she has opinions and she's feisty, and she can be very stubborn," but she and East, 30, enjoy each stage in their kids' growth.

"My husband and I have said the same thing, that right now where Jett is, we love it. We're like, 'Oh, I hope he never changes.' I don't want him to grow up at all," she explains, adding, "But then a week goes by or a month goes by and we're like, 'Oh, this is the best phase. I don't want this to change!' We've been saying that with my daughter since she was born, and we're saying that now with Jett. Every phase is something new."

"It's just so cool, because you see them grow and turn into people," the proud mom says. "It's really fun."