I have a 4th grade daughter and there is always bad behavior in her GT class. Since I've been through this before with my older boys, IMO, 4th grade is when kids really push the limits to see what they can get away with in school and social situations. It's annoying, and just something that needs to be dealt with at that age. Some principals are better at it than others.
One idea-- can you ask the administration to give the class a lesson on appropriate behaviors and inappropriate behavior, and also discuss consequences? In my dd's class, the school psychologist also gives a weekly social skills lesson aimed at further educating the kids on how to properly behave. One thing I've also insisted they do is to notice and reward good behavior instead of just correcting the bad (somehow they never thought of that).
But-- I'll just play devil's advocate here. Is it possible your dd isn't quite as innocent as you think? Your dd said the principal was eating popcorn while she was sobbing. Only you know the context of how your dd told you this, but I think if my dd had been accused of something and was sobbing, the last thing she would notice is how the principal reacted. And you say your son had a similar experience being wrongly accused. Is it possible your mama bear instinct isn't allowing you to see that the kids might be involved? Of course I have no idea. Just something to ponder.
Another thing I might suggest is the American Girl Doll books on relationships. They're easy reads and are very explicit about how to be a good friend, what a bully is, how to react to bullying and when to involve teachers. My dd and her friends all enjoyed them. They might help your dd clarify some situations that have happened and give her the right terminology to talk to or defend herself with the school administration.
