I think people (addicts or not) on some level are very simple: We don't read words as actions. I had told AH that I would leave if he didn't get help with his drinking. It took me four years to actually leave. And he was in complete shock: He never thought I would actually do it.
I heard all of those same things your AH is telling you (and the kids), but I heard them after I left. It's my fault if he starts drinking again because the recovery success is immensely better for people who have family support during recovery; the children need counseling not because they have lived with an abusive alcoholic father their entire lives but because I caused this terrible trauma by breaking up the family, he gets it now and he deserves a second chance.
Basically, what they say is "you haven't been a good enough wife to me or I would have seen the light earlier, but now that I have seen the light, I am in my immense goodness going to give you a second chance at being a better wife to me." Which just proves that they haven't really seen the light. In my book.
You have the right to leave and walk away. Always. Marriage is a contract, it's not slavery. Or at least, it shouldn't be.