How to deal with a toxic parent after you’ve already broken off the relationship

I’ve ended my relationship with my father two years ago. He was abusive towards me physically and emotionally during my childhood. He’s tried several times to smooth things over but I don’t want him to be a part of my life anymore.

My question is, to anyone else who has had to eliminate two parent for their life, how do to deal with family gatherings. My father and I don’t live in the same state but my brother is getting married and I know he will be there. There will be a funeral as well and I know he will be there. How do I deal with him being there when I don’t even want to talk to him? If we are in the same event I know he’s going to try and talk to me.

How do I deal? I’m already getting super anxiety just from the anticipation of the ordeal. Advise appreciated.