I'm angry at my sister for drinking in front of our alcoholic mom despite me drinking as well
But weren't you drinking too?
It doesn't matter I still hate her for it
You are no better than your sister for doing this and you have no right to call her out when you're the one being a hypocrite. Both of you need to stop being selfish and drink away from your mom so you don't influence her.
It's not my responsibility to help my mom get better.
If you think it's your sister's responsibility to not drink in front of your mom, then it's your responsibility too. It doesn't make sense for your sister to not drink in front of your mom if you're still going to.