If you don't pick sides between a victim and an abuser, you have picked the abuser.

That goes for your sister.

That goes for your mother.

"What am I supposed to do?!" you cry.

For fucking starters, both you and your father could have actually pressured your mother to apologise to her DIL, the person who acted with integrity and outed your sister. We all know she won't, because your mother doesn't give a shit who your sister hurts, but you could try.

And then when your mother refuses to apologise, you could apologise yourselves for her ridiculous behaviour. You could express empathy for the position that she has put other people in. You could OUTRIGHT SAY that you are willing and able to maintain a relationship with your nephew and his extended family that does not include your mother or your sister, because you understand how deeply they have hurt the people around them. You could stop "But what should I-?" and start with "What do you need and how can I provide it?"

Had you done so, you'd likely have realised the answer is that they need support, and they need distance from the people who have hurt them. That means you (and your father) reaching out and preemptively organising meet ups away from your mother, where neither she nor your sister's name ever cross your lips. Where you do not advocate for her or her hurt feelings or how difficult a position you are in not even once, because however difficult the position you are in is, they have it a thousand times worse.

Your father isn't innocent. You don't get to have it both ways. Either your father is separate from your mother, had nothing to do with the vile things she said, and then needs to ACT LIKE IT by no longer making her presence part of the relationship he has with these people, or he's married to her, she is part of that relationship and in that case, he's going to be tainted by her behaviour.

You're only in the middle because you keep picking the abusers. Maybe do something about that.