Yes, he does buy/ask if you want those things at the shop to hopefully appease you for what he probably thinks is his "bad" behaviour.
You know, he MAY have acknowledged to himself that he has a drinking problem, some people do, some don't, but it is kind of beside the point, you are the one that has a problem with his drinking. The only question is, what are you going to do about it.
His promises are meaningless, as you now know. Your disappointment is something you can manage though, stop believing him and you won't be disappointed. I truly mean that. Your expectations of him are not realistic perhaps. He is an alcoholic, alcoholics drink, that's the bottom line.
Yes, he sits there on the sofa pondering the good/bad of going to get drinks, but as you have seen, the "good" idea, to him, will ALWAYS win out.
As long as you know that, your expectations will be correct.
I really like your idea of a Air BNB for a week or so. Really this is the best thing you can do for yourself and your children right now.