Sorry you're having a crap time.
The sleep issue sounds difficult - have they agreed to fund the monitor thing yet so that you don't have to stay by her side all night - you might feel that you have more time for yourself then, some evening time etc.
You're seeing paed next week, aren't you? Hope he can give you some answers and some alternative to the sedating as I know that some people involved with dd are very resistant to you doing that (was it SW?) and have told you not to.
Your ILs sound vile in so so many ways. Surely MIL doesn't still think that? Did she just say it when dd was first born? Not that that makes it all OK, but hasn't her attitude changed as dd has got older?
School will have to cope at some point. The respite carers with have to cope at some point, cos you do need time away, and if dd knows that she can yell and then she gets you instead of school/ them, she presumably is bright enough to know that that's the way to achieve what she wants.
I get that you are totally devoted to her, but there comes a point where everyone needs some respite, and if school and respite carers know you're always there to bail them out, they'll use that escape route and not find their own ways to deal with it.
Hope that things get easier for you.