FWN said, "He tells me pretty regularly that even if he fixes this problem and stops drinking, that I will find something else about him that I don’t like."
HOW WOULD HE KNOW?? He hasn't ever stopped alcoholically drinking!
Please do not let him deflect the conversation to "poor me, I've tried so hard" and "you are just trying to control me, blahblahblah."
You know he is an alcoholic. He can NOT moderate his drinking and NEVER will be able to do so. Until he admits this to himself and does something about it, you and your kids are stuck in a tornado.
My heart breaks for you because you must be absolutely exhausted, mentally and physically. You've gone above and beyond trying to fix this for him.
But this is HIS fight now----he has all the resources to win it if he really wants. You must put your children and your self first now.