Hi, and welcome!
As the others said, he isn't "relapsing"--he's drinking. Nothing, at this point, is stopping the progression.
I know it feels like you SHOULD be able to count on him to do a few things, but trust me, you can't. It would be far less burdensome to be on your own with the kids than having this big kid who is more work than the rest put together.
As you have already seen, alcoholics are very resourceful. He'll figure out some way to keep warm. And when he's sick enough of his lifestyle, maybe he'll decide to take all of this seriously. Because right now he's not. And apart from the physical danger his drinking presents when he's caring for the kids, this is terrible for them. I'd suggest letting the school counselor know what's going on at home--the counselor might be able to work with them in an age-appropriate way.