I'm a family law lawyer - i don't say that to indicate this is "legal advice," it's just so you know where my two cents are coming from.
I don't know whether drinking has been an issue in your case to date or not, but I have never seen a judge punish a parent for taking healthy steps to solve a problem. A LOT of parents abuse alcohol. Many don't have your insight and self-awareness. Where I see people get into trouble is denying, minimizing, and insisting that it is their God given right to drink and no one is going to tell them otherwise. I would still talk to a lawyer, and indicate your need for recovery is non-negotiable, and come up with some ways you can stay sober and not jeopardize your case/minimize the impact on your case.