This isn't healthy for you or your kids. I'm voting for you to leave. But give him the chance to get help. Maybe when you and the kids are gone, he will realize that he has a problem. If he won't get help within a month of you leaving, then go your own way, and don't look back.
I'm so sorry you're going through this, I know from experience how bad it can hurt. Phone affairs and physical affairs hurt just the same. And soon one is going to lead to the other.
You may consider talking to someone yourself. Sometimes when you talk it out with someone not related to the situation, it makes it a little easier to wrap your head around.