I cannot address your situation directly, but there are some basic things to keep in mind.
The first is that only your mother can make the decision to recover. No amount of pleading and reasoning will make them change until they WANT it, and that is something that cannot be assured by a mountain of promises. Years of experience and testimony bear this out - summed up in the 3 C's
You didn't Cause it
You can't Control it
You can't Cure it.
Personal experience - My mother died from her alcoholism and drug addictions, and no amount of pleading from her mother, father, sisters, brothers, children or friends made a single bit of difference.
What you can do is establish boundaries for behavior you will and will not accept from your mother as it is directed toward you. For instance "If I visit you and you have been drinking I will leave". I can't say if this would have worked with either my mother or (also deceased) father, but pleading or putting up with the behavior is definitely a losing game plan.
As for your siblings, they also must decide on their own if they want a different life of not. It is the 'leading a horse to water' problem. You can tell them about programs, counseling, books, al-anon, etc. but it is up to them to take that path. You can be an good example and a trusted friend.