I don't want to dash your hopes. I understand that because he is the father of your child (probably other reasons as well) you are invested in him. But so many times we think they "get it"...only to see the sad cycle repeated.
It's nice that you offered to go to an AA meeting with him. But until he calls on his own and says "do you know where/when the next AA meeting is?" he probably doesn't actually get it.
Sounds like he is at the "I don't ever want to face the uncomfortable consequences of my drinking again!" which unfortunately is far from "I don't ever want to drink again"
It's amazing how long and how far down we are willing to go and still bargain with the devil.
Take care of yourself and your child. Giving cash to an addict/alcoholic is pretty much the same as buying them their next drink/hit.