Oh couthy. I've just been reading the thread and catching up. I'm sorry things are so shit.
I've been there with DS1 - with the bad behaviour not the learning disabilities. Everything you describe he did, plus a whole lot more. Holes in walls, screaming abuse at me, climbing out of windows when I grounded him, taking my things if I ever confiscated his, barricading me into my own bedroom to harangue me so I couldn't walk away, smashing things, smoking dope, taking other drugs, truanting, getting excluded, outrageous lies, not coming home on time or at all, attacking me, getting arrested, minor crime...
Everything Maryz says, I would second. Nothing you are doing is working, so you have to try something else. And since you have tried practically everything, the only thing you have left to try is to stop trying so hard: you have to detach from this or you will burn out.
I think of control like this: you can't make this kind of teenager do anything; they have to learn to make themselves. If you try to keep control, they will fight you for it, and you will lose (I think because they have biology on their side). Losing control is damaging, for you and them. A better option in extreme cases like this is to give them control - over pretty much everything that doesn't put you and the rest of your kids at risk.
It feels like giving up, especially if you have been running a tight ship (and I speak from experience here); but in fact by 'letting go' you (a) gain the energy to fight the battles that actually matter and (b) help them move towards the thing they're aiming for anyway - i.e. independence... And it turns out that you keep influence even when you no longer have control.
Some things I learned...
Call the police every time your DD uses or threatens violence outside her own room. What she does there is her problem. (My DS lived on a mattress on the floor in an otherwise empty pigsty for a while, because he'd smashed or sold everything, until his mates embarrassed him into cleaning up).
You only actually have two options: throw her out or hang on in there. I drove myself mad thinking there must be some other solution, but there isn't. Only you know which is right for you: you will hang on in there until you can't any more. It's something you can review in your head at any time: it took the edge off my panic to realise that even if I had hung on on there until today, I could still kick him out tomorrow if things got too bad.
Ignore the nasty manipulative social worker. S/he obviously doesn't know what s/he is talking about. The thing about dealing with this kind of difficult teen is that you weigh up impossible things: rejecting her versus protecting the others. The only reason I didn't throw DS1 out was that I judged that the harm that would come to him if I did was greater than the harm that was coming to DS2 and me while I didn't. If that equation had changed, my decision would have been different.
Get a lockable cupboard or box. Or several. DS2 had his own, in which he kept packed lunch things and treats he didn't want DS1 to take (among other things). It helped him feel a bit more empowered in an otherwise disempowering situation/relationship. It's shit that DS2 needed this, but it was less shit than being stolen from, or never getting his share of treats.
Give DD a concession asap. Personally I would pick curfew times, because 7:30 does seem early for a 15yo, even midweek. Wait for a calmish moment and say something like "I've been thinking. I wonder whether 7:30 is too early for you now you're almost 16. What do you think? Is there a later time that we can both agree on?" Ask her to suggest a time she thinks is fair and work from there. Don't try to pull her down too far (I reckon 9:30 or 10pm is fine at her age, maybe even later) and if she suggests a time that's late for the rest of the family, still agree, but remind her she needs not to disturb the others when she comes in. Remember she will come in when she likes anyway if you try to lay down the law, but if you encourage her to think responsibly, that will pay off sooner or later. Giving her some control early on, and whenever you get the opportunity, shows her you are not trying to "control her life" and that you're now open for negotiations.
Goodness, I have waffled on. I'll shut up now. Hope you have a peaceful night.