"When the news broke, I flipped on Hank and told him to get out of the house," the reality star, 29, told PEOPLE in an exclusive sit-down interview, out on newsstands this Friday.
"But then I allowed him to come back and get Little Hank, because we knew there was going to be this s--- storm. I had to calm down and really just think logically and figure out what the right thing to do was."
Wilkinson called Baskett, 32, and asked him to take their son to New Mexico, where Hank's parents live.
"I was like, you need to take him and just hide out for a while," she says. "But what was so hard about it was that I felt I just gave my son away to the man who'd cheated on his family."
Still, because she had to stay at home with the couple's 5-week-old daughter, Alijah Mary, now 4 months, she didn't have any other options.
"It was so gross to me, but I knew in the back of my mind that he's a great father, and is the only one who could protect his son," she says. "If he'd stayed here, he'd have been hounded. If I took him to preschool, to the movies, I would not feel safe. But giving Little Hank to Hank to go to New Mexico was probably the hardest thing I've ever had to do in my life."
The most agonizing part of the situation was waiting to be reunited with her son.
"Hank never told me, 'Oh, I'm coming back next week,' " she says. "So I was all alone with Alijah. I wanted my son back, but I didn't want to do something to hurt Little Hank, like use him as a tug-of-war item. I had to just allow him to think he was just visiting Grandma and Grandpa. It was the right thing to do."
For more from Wilkinson on the state of her relationship with Baskett, pick up the latest issue of PEOPLE, on newsstands Friday
Reporting by LYNETTE RICE