So my daughter who is in year 8 was in a lesson when her teacher 'cold called' her a question. My daughter responded she didn't know the answer and the teacher then threw a highlighter pen at her, hitting her on the arm. The teacher then did it again to another student, also hitting them on the arm
Your daughter has selective mutism but was able to say that she didn’t know the answer. What was the question? Was it a case that the teacher had only just told the class information and was checking who was listening? Because she then repeated the questioning and pen lobbing to another child. You say the school said it was a game - and it could well have been. Even in primaries, objects (usually soft toys) are tossed between people as a game and/or to signal a turn to speak.
You haven’t really given very much information at all about what the school said in their explanation - is that because it would undermine the whole picture you’re painting? That’s my guess. You wanted all hell to break loose on the teacher who playfully tossed a pen, and when the school didn’t comply, you raised a complaint, and then when that didn’t go your way, you took your daughter out of school completely unnecessarily for a whole day a week. Now you’re drumming up outrage on MN.
You - and your poor daughter - would be a lot better served by asking for a meeting with the teacher (and a member of the SLT) where you or your DD could explain her upset and hurt, and the teacher could apologise to you both and fully explain the circumstances. That would reassure your DD and allow her to attend the lesson.
You’ve made this a hundred times worse for your DD. As a sensitive, shy child I’d have been absolutely mortified if my mother had done this - because it’s making everything worse, and now you have all her peers and the whole school talking about your DD. You’re also modelling helplessness and a lack of resilience.
A bad thing happened. The teacher tossed a pen at your DD and another child and that was wrong of her, but your response is way, way out of proportion. Speak to the teacher and move on - for your daughter’s sake.