My mother has never been good at standing up for herself when she needs to, so as a matter of principle I always fought back for her. My sister always hated that so much - she knows I'm not scared of her and that her words don't bother me during her tantrums.
That's a pretty common Karpman drama triangle. Your sister becomes the perpetrator, your mum is the victim, you're the rescuer.
It prevents your mum from doing what she needs to do for herself.
I used to defend and protect and rescue and try to save my mum, too. It takes a toll that's hard to see when you're the kid protecting (or trying to protect) a parent.
With mine, I just had to stop putting myself in situations where it was almost guaranteed to happen. There was no persuading my mum to stand up for herself, I simply had to change how I participated in the dynamic.
It's very painful to step away from that conflict, but I also wasn't making anything better, just expanding the target area.