Hi Dane,
Welcome and hello

I'm glad you found the site, and sorry for what brings you here. It must be so validating that your son understands his sister is ill and distorting reality. People with BPD tend to break off their bad behavior and project it onto people close to them, it's a form of externalizing very negative parts of themselves that they can't tolerate. When she says that you were abusive, it is likely that she is projecting her own behaviors onto you where she can process the emotions from a safe distance. Unfortunately, this is very painful when you become the target.
It is also possible that she is identifying with her dad because in her mind because she identifies his abuse as a form of strength, even if it hurts her. She may even feel she deserves the abuse because fundamentally she feels like she's bad.
While she is estranged, take this time to talk to people here and learn what you can about the disorder. I found it was helpful to keep reading and piecing the puzzle together until I had a string of aha moments about what was driving the behavior. Often, it is the nature of the disorder, and not something personal, though I know that is hard to work through when you're on the receiving end of the blame.
The skill that helped me stop the cycle was validation. This means acknowledging and accepting whatever emotions she is feeling. You do not validate the invalid, and it can take some practice to tease out the difference. Start with people you know and practice on someone less emotionally charged.
The other thing that happens in BPD relationships is JADE-ing (justify, argue, defend, explain). It never works. Often it just cranks up the speed on their emotional roller coaster because they feel that you haven't heard them, so they dial up the intensity. The antidote is to validate the feelings.
You did not abuse her, and that is all that needs to be said, to yourself and to others. She is in tremendous pain and likely inherited a sensitive genotype from her dad that makes her susceptible to intense emotional states, plus she had a father who punched her Set the guilt aside and don't give it attention. Many of the skills needed to guide these children are not intuitive, and if there was an abusive parent in the family, we are doubly challenged to help our kids.
You're here now and we will walk with you. And in a two for one deal, the skills you learn to communicate with your D are the same ones that can be used with your GD.
LnL