Your story, unfortunately, is not unique.
she won't go because she won't be away from her child
this is not why she wont' go, but none of that matters. I know you love her, but nothing she says about her drinking, the kids, or your marriage matters while she's in this pattern of self destruction.
I would take an emergency week off work, consult with an attorney and do an intervention. Find alternative childcare as she is a danger to your children.
All of this is probably more scary to you than what your current situation is, because we're hardwired to protect the alcoholic, deny the reality of the situation and just freak the hell out instead of taking action that can actually change things.
Good luck. And expect severe reactions from some folks here. Children in danger from alcoholics is, understandably, a huge trigger around here.