What do you get out of this relationship now?. What has been in this for you?. Did you yourself grow up seeing a parent drink too much?.
All you have done here is act out the usual roles associated with such spouses; enabler and provoker (you never forget). Co-dependency is often seen in such relationships as well and I am wondering if you are also co-dependent. Read up on co-dependency as well as contacting Al-anon. Do attend their meetings in person if at all possible as well, at the very least read their literature.
There is nothing you can do to help someone with a drink problem; your H does not want your help and you are too close to the situation to be of any real use to help (not that he wants your help and support anyway). I am sorry to write that but its fact, nothing you have tried to date has worked and it will not either. His behaviours too are likely the root cause of your own depressed state. His responses towards you are typical of the chaos you are really living in, you're just firefighting one crisis to another.
If he is indeed an alcoholic he should not be drinking at all, not even cans only on the weekends. You cannot and must not make such bargains with him.
Telling him to go or saying you want out of this marriage now is not a selfish act. You would be far better off focusing on you and your children. Seek legal advice on your situation re the house and kids and work from properly acquired knowledge, not supposition.
The children, house and mortgage are simply not good enough reasons, not even close, to stay with someone with a drink problem. It just teaches your children bad lessons on relationships and lessons that they could well go onto repeat themselves. What are they learning from the two of you about relationships?. They are learning an awful lot of bad stuff currently here?. Would you want them to have a relationship like yours now is?.