Lots of replies, thank you 
Alita7 "Is her only special need anxiety or does she have something else?"
I, my DH, my parents, 2 of DD1's carers (she has SN and goes to special school), etc., are all convinced that she has SN. I, as my hunch, think ASD, but it could be something else and the anxiety gives ASD type reactions, I guess. Unfortunately, school have responded to my reports (and video evidence) of her anxiety, but they see a smiley, happy child. The Paed has only seen her once, in his office. SALT has shown her pictures, told her that she works with DD1 at her special school (true, but I don't think a fair tactic to build a relationship), talked about dogs (her obsession) and shown her picture tests (her strength). Then have said she's fine.
She's far too high functioning for a state special school. But, within her MS class, she's in the bottom group for maths and middling-low for literacy. She needs lots of adult support in maths (but no IEP, no SEN acknowledged). I think they're not using methods she can get to grips with, but as I don't know what they're using, it's hard for me to help her at home. She gets very upset if things at home aren't exactly the same as school, such as number lines.
I'm reluctant to try another school, because she's only been in this one for 1yr 2 months because I had to remove her from her first school after a completely disasterous transition from yrR to yr1 (she got poorly, massive anxiety about all the changes, then attempts to take her back to school and further illnesses corroborated by doctors lead to HT indicating that I was FII). I suspect that we'd just go through the same cycle - token 'new girl' friendships until they realise that DD2 can't be like them then slowly drift away, massive anxiety, token attempts to calm it, then once that's effective, remove it 
She hates lots about school. Not just the work, but the pressure, the anxiety, the noise, the chopping and changing of what they're doing, the pace, the busy break times, the crushing assemblies (the hall is so small that they have to file in class by class and are sat in a regimented arrangement so they can all fit), the homework, the feeling that she's thick at maths because she's a circle and the class is always told 'and circles, you don't need to do x bit of the homework because it will be too tricky for you' (or at least, that's what she says. It could have been just once).
I've investigated a bit more. There are 5 HE groups in my local area.
We were talking at the dinner table about looking forward to going back to school and DD2 said 'No, I'm going to be a home learner.' I said 'who told you that?' and she said 'I did. I told myself. I decided.' Then she spent the rest of the afternoon before bed time pleading with us to let her HE.
She thinks she isn't going back after the Easter break 