Don't know if this is helpful or not OP but just thought I'd share this in case it is.... my dad has always had a problematic relationship with alcohol. Not sure if he meets the technical definition of an alcoholic, , probably a high-functioning one rather than a dribbling, sleeping in the street, fighting one, he doesn't binge drink and go crazy but he drinks excessively every night and it changes his personality and makes him obnoxious and unpleasant to be around.
Several years ago my brother, who doesn't have kids, wrote him a letter, very calmly, just saying "I'm not going to try to influence you or change what you do, I'm going to let you know that I love you but for my own self-preservation I'm not going to see you when you've been drinking. You need to decide if you are prepared to have a relationship with me on those terms. If you are, great, if not, goodbye." I'm simplifying a bit but that was what it boiled down to.
This was more than ten years ago and it put a huge rocket up my dad's arse. He hasn't stopped drinking, but he basically observes a limit of 2-3 units a night when he's with other people and will cut it off there. And he doesn't drink at all with my DBro He probably is drinking more than that when he's alone, and I'm not going to pretend that he's dry, but he knows that he can't go over that limit when he's around his family and their kids. And its helped his relationship with his family hugely.
The reason this letter worked was because it was very non-emotional and rational. My DB basically laid out the terms on the table, without judgement, just said "this is what's on offer, take it or leave it." And my dad took it. He gave him no excuse to back out, nothing to make him look vindictive or nasty, but made it clear that those terms were non-negotiable.
I don't know how bad you mum is, it sounds as if she's quite bad and it may not be in her gift to moderate her intake. You may not be able to stop her drinking But I do think that when you are trying to negotiate with an addict in order to protect yourself and your family, this approach is quite helpful.