"He admits to having a problem, but has told me that he doesn't want to stop"
There's all you need in your own post.
If nothing changes, nothing changes. You are powerless over anyone but yourself.
If you don't want to live with an abusive selfish alcoholic, don't.
We don't marry someone's potential, we get what is in front of us.
Addiction= continue to use no matter the consequences
Take care of yourself as your body heals and you make the right decisions.