Cheating for me is not a deal breaker. Oh don't get me wrong, it's going to result in broken body parts.
There is so much more OP going on in your relationship. You need to really talk to someone not involved like a therapist, your doctor, minister. I would honestly call a woman's shelter or crisis line. They can get you resources. That is a bad situation. I am not trying to be mean or harsh, you need someone to talk to. A professional, not knocking alanon, but you and the kids need counselling. He needs intense rehab.