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Midnightly -that other girl must have seen someone at home act like that. I'd want to ring her home and inquire if that is how they act in front of her. But seconds later, I recalled something from assertiveness training decades later (I was a shy young kid who did not know what heart on her sleeve meant but suffered for it). Next time the girl with type goes off, your daughter is to tell her: when you act like that towards me, it frightens me and ruins my day. (I'm hoping that saying that once or twice will clue the other child that she's doing something WRONG).
But I still think the teacher should be told so this does not go on without end. As a schoolkid, not knowing when a "bad" schoolkid was going to stop teasing/bothering me/hit me up for change did not help with my anxiety. So offer that assertive line to daughter (she's not to say more to the other child after saying it, to see if the other kid responds) just to see if she's relieved of having a solution to try. Let her know you'll get in touch with the school if this continues after the one day she tries the solution.