I think you've gotten some good advice so far. You'll need to consult an attorney on the specifics for your state regarding what you can do to protect your child. Things are going okay for me right now because STBXAH is living with his parents. The boys stay over at their house for overnights, or he comes here to visit with the kids during the week. Right now I have included language in my divorce complaint related to alcohol problems. I'm not specifically divorcing him on those grounds though. It can be difficult to prove alcohol addiction. (You'll want to document whatever you can NOW if this is the route you need to go, and from your posts, I think that might be best.)
Right now, my STBXAH has committed to not drinking when the boys are with him. It's a part of standard child visitation wording and will be strengthened by the alcohol abuse wording I included in my complaint. If I find that he has been drinking around them, we will go back to court for supervised visitation only. He knows I'm very serious about this. At this time, I'm trusting that he will do right by them. Once he gets his own place, I'll need to reevaluate.
It's VERY hard to balance making sure your children have a relationship with their parent and your need to protect them from his behavior. An attorney is the best place to start. You can also research the laws in your state and find out what standard visitation is.