Inpain, please keep strong. I was like that with my H when he was home, now I don't care what he does. Be there for your kids. Remember that you are the adult here and the only person they can rely on.
My sister told me that she knows two set of kids when the dad had an A/ left the mum. They told her that the best thing that their mother did was/ is to be there for them and they really see who their dads are! This speaks volumes to me.
It's really hard but it is early stage for you. Keep faith. I can assure you that it'll bet better :-)