YABU because you are facilitating her behaviour. YANBU because she's your mum and she's a bully and she has maltreated you forever and you've been traumatised and it's scary to even think about standing up to her, let alone actually doing it!
It won't ever change if there are no consequences. The reason your mother behaves this way is because everyone allows it. If people didn't allow it, she wouldn't do it.
I'd invite her stipulating that she cannot drink. If she asks why, I'd be honest and tell her I don't want the drama. If she rained down hell on me, I'd uninvite her and go no contact.
I had to do the same with my mother. Alcohol wasn't an issue but her behaviour used to be atrocious.
She's as good as gold now, for the most part. And when she isn't, I tell her what she's doing, why it is unacceptable, and go no contact.
Life's too short to put up with other people's shit, regardless of who they are. It seems scary and impossible but honestly, afterwards you'll wonder why you didn't do something years ago. And your sister should do the same. Yes, she needs somewhere to live BUTyour mum needs her rent/keep. Your sister should respectfully, calmly and non confrontationally explain to your mum that things need to change - somewhere neutral and public. If your mum loses it, she should just walk away/leave.
When I started down this road with my mum it took a few months for her to realise I meant it - I wasn't going to take her sh#t any more. I stopped calling her. When we did speak, if she started I'd give her 2 warnings, nicely, but firmly telling her if she didn't stop I'd put the phone down. I'd tell her again and then if she carried on, I'd put the phone down. It's hard but for us (I have siblings), it worked. She used to get physical as well and the last time she did, I squared up to her and begged her to do it again as I had 40 years of hitting back to unleash. She knew I meant it (and I never hit anyone, ever but I absolutely mean it). She's never threatened to hit me again since that day - textbook bully response.
I'll be honest - it took about 2 years to see the positive consistent behaviour changes. It was like training a pet or teaching a child. Repetition, consequence, reward etc. She hardly ever reverts to old habits and if she does, I immediately shut it down or simply leave.
They're our parents but that doesn't mean we have to accept their behaviour. It's toxic and bad for us and those around us. You think you're shielding your children but they must pick up on it. I refused to let that carry on down the generations.
Tip toeing round her is not helping anyone. The reality is, unless she's made to understand that her behaviour is unacceptable, she has no reason to change it and she won't. It's that simple.
I'm really sorry you're going through this and I wish I could transfer the experience of the last 20 years I've had, over to you so you could see and believe this is doable. And for the best.
Sending you strength and hope all goes well.