Hey there. I hope I can help.
While it's been said before, I don't think reaffirmation that this is indeed abuse can be a bad thing.

I certainly feel for her mental illness...but that doesn't give her the right to make your life a hell, you know?

Her behavior towards you is inexcusable, and I'm sorry you had to suffer through it.
I understand your mom's situation, but I do think she should've taken a more interested role in trying to help you. Unfortunately, your sister did a great job of putting her in a hard position...while burden of proof falls on the accuser, an investigation by CPS is a hard thing for a parent.

I think she should've helped you regardless, and I think you'd have a right to resent her to an extent over it, but I do understand her situation and rationale. Again, I am only sorry you had to suffer for it.
I think it may be best to distance yourself from her. You can only do so much in regards to trying to foster a healthy relationship with her, but it can't be at the expense of Wiltedrose either, you know?
You are in my prayers. I wish you my very best.
Hugs,
Harley