I am sorry. I understand your struggle. However, I think your kids are seeing things a lot more clearly than you are. They need you to protect them and to do the right things for THEM. They are first, no matter what.
He is not drinking....much. Well, that says a lot. An alcoholic cannot drink...AT ALL because it will change and progress. He is doing this now b/c he knows you are on the fence.
I am sorry. Stay your course. Give yourself time to heal, and above all else, put your children first.