The short answer is: You can't.
She has to help herself. That starts with her admitting that she is alcoholic - but then she has to actually WANT to fix it.
It isn't an easy road. My brother had 5 de-toxes (one a residential 3 month course that he discharged himself from after 6 weeks).
He lived with me for 2 years after my SIL divorced him for the sake of their 6 year old son. I cared for him, I kept a roof over his head, I fed him, I drove him to meetings every Monday - Wednesday morning (after which he went to Weatherspoons for a drink!)
Al-anon was my saviour because I learnt that I couldn't cure him and he was on a road to destruction whilst he continued drinking to excess.
He came out of his 5th detox on a Tuesday - and I suspect he was drinking again by Wednesday but he denied it. By Friday he was prostrate at the bottom of my stairs not able to move any further from the front door. By Monday the police arrived at my door to say that he was dead at the top of the road - he was on his way home but alcohol toxicity had got the better of him.
Of course I grieved for my clever, lovely, witty brother: the athlete who was a cycling champion.
I have never grieved for the alcoholic brother who would stumble out of a taxi, not manage to get his key in the door and fall asleep under the shrubs in my front garden. The brother that I would have to drag into the house the next morning before my neighbours saw him in the front garden.
When I had to identify his body, I was allowed by the police to go into the 'showing room'. I remember I approached him as said, "Well, what have you done to yourself this time?" and I kissed his head.
You see, Al-anon taught me that I was NOT responsible. I could accept his death as something that was HIS responsibility. And when the inevitable came, I was able to cope.
Then I had to start to phone the family to say that DB had died - and it definitely was him because I was just back from identifying him ..... but that is another story!
OP, please think about going to a meeting or two with Al-Anon. You don't have to go every week. You can go and not speak, listen to others. The group will probably be pretty much established by the regulars, but I was so welcomed when I walked through the doors with trepidation. I remember a very kind lady who said, "I have noticed that sadwidow is nodding a lot to our stories and updates. Sadwidow, would you like to say something? It is up to you."
OP, I hope that this helps you in some way to see that your mother's alcoholism is NOT your problem and there are RL support groups that you can tap into if you feel it would help you.