C.C.
I think I could have written your post a year ago. My younger daughter's nickname is "Bee," which is short for Busy Bee. She is always on the go, and lives life out loud.
It was the same deal for us at preschool, where the teacher came to me expecting me to resolve my daughter's issues while my daughter was at school. I pointed out (nicely) that I bring my child to school ready to learn. She is clean, dressed, and fed, and has a healthy respect for legitimate authority figures. What happens once I drop her off is the teacher's responsibility. To think that I am going to have any kind of effect on my child when I'm not present to correct her is pure insanity.
Well, it continued on where the teacher kept complaining to me that Bee was misbehaving in class, so I went to the Director and said, look, WHAT is the issue here? At home, my child listens to me. So this is not a case of my kid being unruly and bratty (believe me, I'd be the first to admit if it were). The director observed the class and agreed with me. The teacher ended up being removed from the position (not completely due to our situation) and the new teacher had no issues with disciplining our child.
So... ultimately, your job is to bring your child to school ready to learn. It is up to the teacher to enforce discipline in her classroom. If that's not happening, you need to address it with the teacher and then the director. If they can't/won't address the issue, then switch schools.