I am sorry. It seems she is in the belly of addiction. Let go of the anger and pain....she is gravely ill and hopefully regardless she is able to see her daughter at some point.
I know that doesnt seem like much and maybe not the best response from me...I dunno
But if she indeed has alcoholic liver disease given a yr to live and she refuses to quit for her health....the worst is to come. Sadly....her life could come to an end at any point in time even as I write that I cringe.
I would be there for her daughter and confort her and explain that her mother is sick...at this point if she refuses to quit then the most anyone can do for her daughter is to help her heal.
After all in a yr from now who will be left with the pain and burden of her mothers addiction? ...her and she will need from here out all the love and counseling she can get.
I hope my words arent too blunt or upsetting.