That's pretty mature of your son to be able to see that the ABF's word is just that- a word. Not matched by actions. I put my AH before our kids (not consciously and intentionally but I did it nonetheless) for too long and no matter what he tells me now, I'm not allowing him to return bc my kids well being matters too much to me. Maybe your son leaving is your "bottom"? and I hope that you will believe that you deserve more than to live with the rollercoaster of your ABF. If he wants help he can get it and get sober without living with you. You can always find another BF. You can't replace your son. I'm glad that your son's Dad is a stable place for him to go bc if he had no choice but to stay with ABF in your home that wouldn't be good.
I'm sorry you're hurting and I'm sorry for the hurt and confusion your son must be feeling. I felt betrayed by my parents promises over and over as a kid and that's left a lasting legacy of problems with me.