strongerwoman; i sympathize with you and your situation and your children. the fact that you worry about your ex husband using this to get custody of the kids should set off big alarm bells in your head. i think you and many of us on this forum know too well that it is NOT in childrens best interests to live with an alcoholic/addict. as much as you may believe you care for the current guy, you should put your childrens development first.
Unless your ex is also an addict or has some criminal/significant psychiatric history than think about it, he is paying so your/his children can grow up with an alcoholic.
Not that I am siding with him, but i most certainly am not siding with a parent that knowingly allows their children to live in an environment with an alcoholic.
I do wish your children a better future and for you also.