This answer assumes this is a public school. Most of it will be applicable to private schools as well, but there are some important differences, particularly in the power dynamic. This answer is also from the point of view of a parent, not an educator, but a parent who has managed conflict with their school effectively.
One of the most important things to do when talking to your child's school is to come to the table with a positive, constructive attitude, and to make that clear from the outset. Decide, before you go, what you hope to get out of the conversation, and be realistic; don't go in expecting to get everything you would want in an ideal world. Rather, focus on what is achievable right now - and usually in that first conversation the goal should be discovering what is achievable. Also remember that the people at the school are, well, people; they have reasons for doing what they do, and some of that is due to having information you don't have, as well as motivations that may not perfectly match yours - without being unreasonable, necessarily.
In this case, you need to decide between a few goals. Is the purpose of the meeting to find out why they made the choice they did? Do you want them to know how you feel? Do you want them to take a concrete action (for example, when you say she was sent home was that an actual suspension - in which case you might want that removed from her record)?
In the first case, finding out why, the best approach is to be open. Something like, "Hello [P], Would it be possible to meet about [D]'s recent assignment? I would like to find out more about what happened so I can best support her learning at home. Thank you." is best. This has a few things in it that are important for getting the most out of the school:
- Open attitude - not making judgements
- Asking how you can best support the school
- Directly connected to a recent issue
Then in the meeting you would mostly listen. Ask for a summary of what happened. Ask for why they chose to take the actions they chose. Ask what specifically was objectionable. Ask what she could do differently in the future. All of this is asking - and asking without including a judgement in the question. This is quite difficult to do - so formulate your questions ahead of time, and don't deviate from them. Don't interrupt, and don't go too far into the followup here - if the point is to find out why they took these actions, just find that out. Then decide on any further action at home, when you have time to think!
If you want to have them take concrete action, the best approach in my opinion is to start with a fact-finding meeting like above. Then, come back to the school a few days later with a carefully crafted message incorporating what you learned in the fact-finding meeting, politely asking for particular actions to be taken based on your reasoning. It needs to be polite, and it needs to be specific and concrete; and it needs to be thoroughly grounded in the school's policies, as opposed to political theory.
It should also be relatively easy for the school to take - don't ask for something that's either hard to do, or would involve conflict. The school administrators will tend towards what they think is the path of least resistance; make that path doing the thing you want! This is where being slightly annoying is helpful, but only slightly - on the level of making it clear what it will take for you to go away and stop emailing them.
If, however, you mostly just want them to know how you feel, the best approach is a politely worded letter letting them know how you feel. One that doesn't suggest any action, and doesn't require a response beyond a "thank you for letting us know". It should not accuse anyone of anything, and should be very carefully worded to not impugn anyone's motives; simply state how you feel, something like:
Dear P; Based on what happened with the video last week, I wanted to let you know about the concerns I have related to how that was handled. My daughter worked very hard on this project, under my guidance, and we felt that she designed an effective presentation that put every part of our history together. It was very disappointing to learn that not only did the P.A. disapprove of this work, but that, rather than coming to me and discussing their concerns, they [did x y z]. I would like to support my daughter's education in every way possible, and support the school in their mission; I certainly do not want to cause strife in the classroom or the school. I am concerned that my daughter will not feel safe sharing her ideas or beliefs in the classroom setting as a result of how this was handled. Respectfully, Dúthomhas.
The important part here is making it clear how you feel - and in how those feelings impact the school - while underlining your respect for the school and its mission, and your role in her education. Keeping it as positive as possible, while still making your very real feelings known, is important here. (And I'm just approximating your feelings here - this is mostly how I would probably feel in this instance.)
Hopefully the TL;DR is clear by this point - communicate with the school politely, and be very clear in your own mind and in your communication with what your goal is from that communication. Don't break into the legal side of things unless you truly would go that route (which I don't encourage); and don't cast blame. Especially don't blame specific people - then you get into where people have pride involved, and that makes it far less likely to accomplish your goal.
And, do consider your child's wishes here; whatever you do, keep her out of it, since that's what she wants. She's old enough to have some understanding of the impact of this, and given you've raised her to be thoughtful and understand her role in society, you should give her that choice.
