Please remember, he may not mean a lot of what he is saying. Alcoholism causes total insanity. Seen it a few times in my AH. It hurts even though you know it's the alcohol talking still.
I hope the rehab works for him. If I were you, I would have left it up to him to contact his work and his ex-wife re: child support.
He really needs to go into rehab for himself and not to keep a job or a relationship, or stay out of jail. He has to do it for him and him only.
My AH left rehab twice early, it was so heartbreaking. Right now he is in an outpatient rehab program and attending AA meetings nightly on the nights he doesn't have outpatient rehab meetings. I am seeing more improvement in him doing this program than in the inpt. rehab.
But rehab does increase your knowledge. Realize that rehab is just the beginning of a lifelong fight against alcoholism. There may be relapses after this.
I hope things start to clear up for you.
Alcoholism can turn life into pure chaos.