I'm going to throw some stuff out here. They're just ideas and maybe not good ones. So...
He's not a great dad and role model if he's mooching off you.
You're an alcoholic. You're dealing with it. You don't have to be a doormat. You're not subhuman.
Talk to a lawyer.
If he threatens to take your daughter away, call his bluff. Okay, fella, go ahead. I'll be over on visitation day.
He needs to bring some money in. (he's living with you why??) I don't care what else he's doing. He needs to make some time to GET A JOB!
Oh well, like I said. Just thoughts.