I just wonder if it was as categorical as directly telling/asking you to move the appt, or more of an enquiry about if it would be possible, followed mpby more explanation of why they were asking.
Not knowing about your DDs condition or how urgent having the treatment is, I think that if you had happened to me, when arranging the appt I might have mentioned that SATs week was X and if the following week was possible for the Op, that would be helpful.......but that's because Inwould be keen for my DC to do SATs having done the work, because I would be keen for them to start secondary with them behind them and their targets based on SATs like everyone else.......so if it wasn't urgent, I too would be keen to sit them.
DD won't avoudbtheboreparation and stress of preparation anyway. She is doing well and may well get satisfaction from sitting them and doing well.
Of course these are very close now. Changing the date may well not be possible at this point, but if you did want to consider it, you could ask and say why. It is true that hospitals can't just give everyone the dates they would like, but I think they would understand about SATs if you asked...whether something else that would work could be found, is another thing, as is whether like me, you are actually keen for her to sit them or avoid them instead.
I would be surprised if the school just instructed Op to move the treatment....I would think there was more to what was said than that, and that it was more of an enquiry about the possibility than anything else.....quite different. However, I wasn't there, so I don't know.
Anyway, just a slightly different perspective on things and questioning of exactly what was said.
Op, regardless, I hope your DD is back to better health really soon.