Hi Befuddled, sorry for what you're going through. I'm sure others will answer you with much more experience and wisdom than me, but what stood out for me in your post was that your boyfriend is nowhere near ready to get sober. He is doing everything he can to be on his own so he can drink, as I'm sure you've worked out for yourself.
I think you've done the right thing by stepping away as you can't force him to stop and you have no future with him until he does. He's in the grip of something he can't control at the moment and you're not on his radar.
I know it must be painful, especially with the children involved, but I think you're strong and wise to leave this early in your relationship.