Wobbles, I would do the exact same!
I will not tolerate my kids bullying others and they will definitely have restrictions if they do so.
I am not so concerned about my daughter, quite truthfully, but, then again, years can change a person.
I do wonder about my son though. At over 4 1/2 he's a little toughie, but, again, boys like the rough and tumble part of play and it could just be that
Many times a bully becomes a bully because of his/her upbringing. Nowadays, both mother and father work outside of the home and by the time they get home in the evenings, they truly don't have the energy to spend with their kids. So what happens is that the kids feel neglected, etc.
Other parents are just bad parents...parents who do drugs, etc. and are not good role models to their children.
Some just don't give a damn about what their kids do.
Yet, at the same time, I do know that no matter how great your parenting is, a child can change. Peer pressure isn't easy on a child either.