Are your kids in therapy? I think they could definitely use it. I think it's a bad idea to stay together "for the kids." If he's a good father, then he'll make sure he sees his kids even if you're separated or divorced. He'll also pay financial support. The kids aren't going to not have problems just because you stay with a man who has hurt you so much and blames you for his actions.

Like Always said, if he had problems in your marriage, he should have talked to you about it, and not strayed. He has no right to blame you for his decision.