Is it ok not to talk to your cheating spouse for a long time? even tho there's a kid involved?

My wife cheated on me left me for another woman she tried to work things out but I just couldn't take her back. We're now divorce and share custody of my little girl. I hate seeing her I don't even want to speak to her or answer her calls or text I just don't want anything to do with her, I sent my brother to pick my daughter and drop her. It just hurts for her betrayal and she thinks I'm doing wrong. I know I should be working together for the sake of our child but I really don't want to.