So? Do your kids need the full truth here about what goes on between mom and dad?
I get how much it absolutely [censored] to not tell your kids the truth, but this is about them, not you. Don't LIE to them, but they don't need to know the details, either. One thing you absolutely CANNOT ever do is poison your children against the other parent. Don't. You will hurt them. Quite likely for life. And you'll damage YOUR relationship with them.
Kids are smart. They'll figure out the truth on their own. And they'll love both of you anyway, because they're both of your kids. Would you honestly have it any other way?