OK, assume you could have nagged him less and he'd still be there. What about his going out and leaving the house and kids for you to take care of? Are his feelings more important than yours? There are worse things than being a single mom--and being a mom with an active alcoholic husband is one of them. In my experience, there is NOTHING as lonely as living with someone who is either out all the time or "checked out" when he is at home.
Have you consulted a lawyer? That should be your first step. He is responsible for supporting his child, and you need a custody/visitation order in place.
You'll get through this.
Oh, and welcome. Have you been to Al-Anon? If not, this would be a GREAT time to begin.