Hello Lunaloo, thanks for getting back, but your mother is in denial, she believes she isn't doing anything wrong and when you try and talk to her, you have to either believe her or refute what she has to say, because everything she will say will be in her favour and deny what you've had to say.
You are really a caring person and indeed want to help her, but as an alcoholic, she knows what she is doing is OK and poses no threat to anyone, that's where the problem begins as she doesn't think she needs to see her doctor/counsellor, and at the moment wouldn't pay any attention to them.
If you ask your uncle for help, she may only agree with him and promise she will cut down her alcohol intake, unfortunately, she can't be believed because as soon as he leaves, back she'll go or could turn into or already is a cupboard drinker, hiding alcohol in different bottles ( white vinegar), under the mattress or in draws etc.
The problem is you could tell her or try and talk with her until you are 'blue in the face' in trying to convince her but all to no avail, but her brother gets on well with her then it's certainly a chance.
Is it possible she could stay with him for a little while or vice-versa, he stays with you?
Good to hear back from you.