"More likely to relapse"?? He's in full-blown relapse now, with no signs of stopping.
And unless you are having him bring home a signed attendance sheet or are going with him to the meetings (neither of which I'd recommend), you have only his word that he's going. How reliable is that?
He's not going to be accepted at any "sober house" unless he's been sober--they generally take people straight out of rehab. They aren't places to GET someone sober--they don't do detox and they aren't rehabs. They are post-rehab places to reinforce the skills needed to live sober.
I'd suggest you put your energy into making a plan to live without him--at least for a while. You are in an unworkable situation right now. Your kids aren't safe and you are at the end of your rope.