"It's really tough for them," a source close to Rossdale tells PEOPLE of his sons – Kingston, 9, Zuma, 7, and Apollo, 20 months – with Stefani.
"Every day there's a different story. He is concerned about the kids and wants to keep them safe and is trying to keep all this craziness out of their lives and keep things as normal as possible for them," adds the source. "He's just all about being the best father he can be for them."
Rossdale, 50, and Stefani, 46, announced their divorce in August, when they told PEOPLE in a statement: "We remain partners in parenthood and are committed to jointly raising our three sons in a happy and healthy environment."
Since the split, both exes have begun to move on. As PEOPLE confirmed exclusively with a source last week, Stefani is dating her Voice costar Blake Shelton.
And the No Doubt rocker has also expressed concerns about the kids seeing their parents' names in the headlines.
"I never said nothing about being in a new relationship. I don't know who said that, but somebody did, and then my kid came in last night to tell me about it," she told San Diego radio station 93.3 on Tuesday. "That's how crazy my life is. People can just say whatever they want, and then they can just believe it."