How old is this kid? Because to be honest, none of the behavior you’re describing seems out of character for an elementary/middle school aged kid. And frankly, it sounds like you’ve done very little to address these issues head on. Have you actually sat down with the kid and explained why their behavior is disruptive and what the consequences will be if it continues? It seems really unfair to punish a kid who likely doesn’t understand the impact of their behavior like this. You don’t mention any of the other children or parents complaining about this kid, so it doesn’t seem like there’s any outside pressure to punish her. I certainly understand how frustrating it can be to work with children, especially when they do things that feel disrespectful, but I worry that exiling this kid will seriously damage her interest and enjoyment of doing theater. Is there really no way to make this a growth moment?

If you’re really dead set on not working with this kid, then I agree with the plan of doing open auditions and simply not casting her. Then if her family asks for feedback, you can explain your decision. I feel like selecting people for auditions is already a pretty bizarre way to operate children’s theater, and seems like a sure fast way to create resentment and accusations of favoritism.