Hey darkhunter. Wow, it sounds like your mom's drinking is having quite a powerful impact on you and your entire family. You're sister is going through a whirlwind of emotions too, from the sounds of it. This is not healthy for either of you.
I'm just wondering how old are you? Last year of high school-ish?
Have you ever thought about Al-anon? Just to have a place to acknowledge the tremendous stress your mom is creating for you. It sounds like you've done everything you can - you've even accepted that this is going to leave a scar on your life. It sounds like you're at a pretty low point if it's come to that - accepting that you are 100% powerless to change your mom. But even that's not going to be enough, because your mom is still going to continue to act irresponsibly and she will continue to hurt you. So what can *you* do to help how you are dealing with it?
If Al-anon isn't your thing, find out what services are in your area that provide counselling (they exist). Especially if you are young, the ministry of child and family services may provide access to a counsellor for you. They might be slow (government stuff always is, it seems like), but you will get to talk to someone eventually. If you're not in Canada, start looking around the nurse's station for pamphlets - even on depression. Ask the school nurse or counsellor for advice (IMO school counsellors aren't there to emotionally support students, so don't expect direct help from them). Either way, the important thing is that you find a safe, healthy way to get your frustration with your mom OUT. You don't deserve to carry it all inside all the time. What about you and what you want for your life? How can you possibly make good decisions for your future when you can't even concentrate at home because of the drinking?
If talking to someone face-to-face seems too intimidating right now, there's still other things you can do for your own benefit. Journalling is one idea. Take some time to write down each day how you are feeling. You don't have to keep it, and it doesn't have to be an essay. Just write. It will help unload some of the frustration.
The other thing you can try is read. There are some excellent books out there for Adult Children of Alcoholics. If you're interested, I can message you with some recommendations that worked for me. People have gone through what you're going through now. It might help to read about their stories, and draw some anecdotal evidence for yourself. This forum is certainly a wealth of valuable experiences shared.
This may seem like a lot of work that's totally unfair. After all, you're not hurting people, so why should *you* have to be the one to make the changes? Look at it this way. Part of becoming an adult is learning how to take care of yourself. And since your mom is not teaching you AT ALL, the only thing you can do to make it fair is learn to help yourself. You can't change your mom, but you don't have to accept the scar for what it is now either. Don't let her steal from your start on life.
As for dealing with your mom at home... One thing I started saying to my AF who had to be tanked at every special occassion was, "I'll talk to you when you're sober - not when you're drunk." It was one tool for minimizing toxic conversations. It made him angry, but at least I didn't have to listen to the hurtful barbs that he wouldn't remember saying the next morning.