To whole situation is—forgive my language—absolutely screwed.
@author, things need to be handled through logical steps and a gradual process—there simply isn't a quick or easy fix here.
As I mentioned before, please seek legal counsel; you have access to those local legal aid forums, and surely there is someone there who can point you in the right direction. But you really need to arm yourself with saint-like patience.
Your sister is only six years old—she'll be starting school soon—which is only going to make things even more complicated.
I honestly don't understand why you're feeling sympathy for your mother; she deserves nothing less than being reported so that her custody can be revoked. This shouldn't be viewed as a punishment, but rather as a way to ensure the child is placed in a reasonably stable environment. Please don't hold it against her if she doesn't fully grasp the gravity of what's happening—she is only six, after all. And frankly, it wouldn't hurt you to distance yourself from this toxic environment and focus on fixing your own life. You are twenty-four years old—you aren't obligated to fulfill your mother's duties, which, based on what you wrote about how she brushed you off when she met her current husband, she was clearly never actually acting as a mother to you. You stepped into that role at thirteen—a role you are now performing for your sister. It is truly commendable—I would do the exact same thing for my own sister—but both you and your sister deserve for this to happen in a healthy manner.
A brief side note regarding the accusations of trolling: even if this specific case were some kind of troll story, there is absolutely nothing funny about it. These types of situations are the grim reality for many families. I see nothing wrong with discussing this and trying to offer concrete advice—after all, someone reading this might be facing the exact same struggle.