It's a shame not only that you are dealing with all this, but that you can't get any support from your mother. It seems like she just wants to hide her head in the sand and pretend none of this is happening.
When the **** hits the fan, she is going to be in serious trouble. Perhaps just as bad mentally as your sister.
Because it will hit the fan eventually. A good thing about addicts with kids...they never get away with it for long, because of the welfare of the children. The kids get taken away before it is too late. At least if they want to go down after that, they are not taking the innocent children with them.