Thank you ApocalypseSlough & Inyournightdress - I didn't mean that to be all "look at me, my autobiography would have a sepia cover SEE HOW I HAVE SUFFERED" (etc etc self-absorbed irrelevancies blah) really was just trying to stress how important it is to make sure she gets treatment.
Well done (in the least patronising way possible!) for talking to your DD about this Inyournightdress: I know it must have been an incredibly difficult conversation to have. But you did it - if you were "a horrendous mother" you wouldn't have; and you wouldn't be so determined to get her help.
You are absolutely right that your DD is lying & deflecting. She is trying to protect her eating disorder (which from what you've said sounds to me like anorexia type two, the subtype which includes [binging &] purging as well as the extreme restrictive diet everyone associates with anorexia - that is mere speculation/guesswork however!) & she's lashing out. She doesn't hate you. She is hurting, as you say, for the reasons you say - but also because, at the moment, inside her head won't be a very nice place to be. Living with anorexia means having a voice in your head constantly passing comment on everything you say/do. So right now I have a whispery-hiss of "ugh, like ANYONE wants to hear what YOU want to say fatty... seriously, you shouldn't be commenting... oh & missing ballet today? Don't think that trying to distract me by doing this in-between organising stuff for the weekend will work..." (with a crescendo into a kind of screechy rage from the hissy whisper... my anorexic voice has some serious anger issues...)
Of course the "ED voice" is, well, the person with the eating disorder. It really REALLY doesn't feel that way at all. And it can be helpful, I think, to understand things like the "snoopy old bitch" comment as being that voice not your DD's. That voice can be positively brutal to anyone it thinks is threatening it.
Getting a GP appointment ASAP is important - she will need blood tests doing. Has she been to the dentist recently? If not you might want to book a check-up to make sure there's no sign of damage to her tooth enamel from the vomiting. I agree telling her House Parent is an important step: are you able to meet with them to discuss it? As the school take boarders, have they a plan for managing the care of pupils with EDs [& can it be adapted for your DD]? On the freak!front, with Eating Disorders being ever-more common, maybe you could have a look at the b-eat site [together] & also get her House Parent to help reassure her.
And now, given I've spent actual hours writing