S.L.
I had the same situation with my son. There was one child he didn't want to invite for the same reasons. I told my son to put himself in the other kids shoes. How would he feel if he was the only one left out. I think it may cause more problems between the two children. The child would be upset being left out and therefore bully more. We invited the child and they didn't come to the party which was fine. My son later told me he was glad he invited him cause he didn't want to make anyone feel left out cause he wouldn't like the way it felt. Think about what the child's story is. Maybe there is a reason behind the behavior that you don't know about and showing them some compassion may be what they need.