In a nutshell Bd your sister is not going to change her drinking habits until she herself wants that change. Hackneyed I know. But still it's true.
Would it be possible for both you and your mother to talk with her about impact it's having. Has any discussion ever taken place?
Sometimes, not always, it takes the standing firm by family members to incite this change. Others making it clear what they are prepared to tolerate. And if the standing firm does not work in having her consider change, at least you no longer have to tolerate it. The consequences of excessive drinking....for your sister. Consequences can incite change too.
Sorry about your Mum. Its not fair. Someone needs to say something when the drinking gets in the way of other people's lives.
Look after yourself.