I can only suggest leaving. Unless the two of you are willing to go into intense counselling, I don't see any hope for you two. He has beat you up and there is no excuse for that. He has cheated and you have forgiven him, yet he continues to cheat. You are not happy, staying for the kids is not worth it.

Your kids will suffer far more if you stay than if you leave. Do not listen to your family and friends, they do not have to live with him. Your kids will be grateful in the end if you leave him. Do this for them, do this for YOU!

BTW...asking you to keep your marriage a secret is disgusting.