First, can you get any medication or melatonin to get her to sleep? THen everything would be a little easier. Its very hard to make any decision or be remotely consistent in how you feel when you are sleep deprived AND looking after a baby too. I don't know how you manage. I would also contact Socci's legal eagle and speak to the NAS Helpline.
Now, sorry this is so long but maybe some might be useful:
We seriously looked at residential school for DS last year (he is 10). I don't think many residential placements are "in borough" and its very common for people at residential school/placement to be from all over the place, this seems to be how it generally works.
WHat I think you need to do is build a case, especially as funding is much more likely if its "tri-partite", i.e. Health, Soc Svs and Education (mind you, not sure she still comes under Education at her age).
We started out discussing it with our Paediatrican who suggested himself that we should consider it so obviously he was supportive. I have heard from another parent that if the Paed is supportive (maybe its just this specific one, I don't know) then you are VERY likely to get agreement. Then I spoke to DS's Educational Psychologist, sobbed on the phone, and told her we were seriously considering residential. I told her that we don't WANT to send him to residential and we would much rather not but we were feeling like we had no other option. Next I went to see my GP who prescribed anti-depressants and referred me to the Surgery's Counsellor. The GP also wrote a letter (at my request) outlining his understanding of our situation. All this was completely genuine, not just a plan to get my way iyswim. I had been keeping a diary on and off since things had got very bad, just in an exercise book on the kitchen table. My god, this seems to have had the most impact on everyone!
By coincidence DS is due to transition to Secondary in Sept 06 so this all made sense, to be considering and researching residential, but it really was just a coincidence and convenient. We visited a couple of schools, one we liked and one we didn't (we're in London, one school was in Stoke and the other in Doncaster!). Just those 2 visits helped us decide that residential is too drastic at this point, although we are under no illusion that the day won't come. When your child is in residential school/care they are technically "looked after" (the PC term for In Care) so it is a big step.
In the meantime I had found out about a fairly local NAS school that does residential respite at weekends and holidays so we decided that this would be an ideal half-way house for us to try him in residential but very limited and giving us a break from him (which we haven't had for years and years). It was suggested at the Review that I write a Parents' Input, I don't know why I hadn't already been asked or thought of it myself, and once I had written this it also had a huge impact. Everyone got a copy of everything, my handwritten diary, my report, GP's letter, Paed's letter etc. As we were now asking for DS to stay at his current school (which is considered expensive but is half the cost of residential) and for one weekend a month residential respite at the NAS School it has all been agreed.
I would be VERY happy to send you my report or anything else that might help. Although they're different kids and different ages, some of what I've already written might be relevant, why invent the wheel again?