My 4-year-old daughter bullies other kids. Is that normal?

Some bullying is part of normal development. But when the behavior is frequent, you should teach a positive replacement behavior. Several times each day you should have your daughter practice being considerate to others. Teaching her to say "Please" and "Thank you," instead of grabbing things and running away. When you see her bullying, give a negative consequence. (Put her favorite toy in time-out, for example.) Be firm with your daughter without turning into a bully yourself