One thing I think you’ll discover more as time goes on and you have your healing journey with a professional is that your forgiveness you feel with your mother will wear out. Your mother is absolutely as culpable as your father for not protecting you and your siblings. She’s made her position to you that your gross-ass father is more important to her than her children. She’s made this clear with her words, her actions, and her in-action.
By letting your dad verbally abuse his daughters, she’s effectively endorsing them. Keeping a relationship with your mother will bring you nothing but pain until you have years of therapy under your belt.
I’m sorry that this is reality. You don’t deserve the treatment they’ve given you and your siblings.