Zoo - I'm in a rush but I'm really feeling for you with DD2
I know it is hard to give more attention etc and it is not possible to have so much support from DP as you would like!
My suggestion would be: Put 2 youngest to bed tonight. Then sit dd2 down in kitchen with drinks ( hot choc or squash or whatever you have she likes) and chat. Try and keep a really calm voice (hard I know when you are feeling so angry) Tell her about how tired and angry you feel when she acts up, rather than just demonstrating it! Use "when you do.... I feel .... sentences" Ask her how she is feeling when she is acting up, if she knows why she is being such a monster doing all these things. She may knot actually be aware of why but encourage her to keep talking about her feelings and accept what she says about her feelings even though you don't accept her behaviour. Use "so what you are saying is that you feel... when I/dad/db do...." type sentences. My guess is she is feeling overlooked, having less attention than other dcs - this may not be actually true but it may still be how she feels.
Ask her what she thinks could change to help her feel better. Hear her out on this even if you don't agree with suggestions! Then explain to her that there are aspects of her behaviour that are going to stop. Be very specific about this eg - Waking anyone in household before 7.00am, deliberately winding up siblings, taking/breaking anyone else's toys, trashing room etc. Give a clear example of consequence that will happen every time she does one of the behaviours ( Pick something you know you can carry through on - maybe taking away her nintendo DS for half a day?) It actually doesn't matter too much what it is you do as long as it is something you can do consistently! Reiterate that being in a family is like being in a team. Everyone has to pull together. ASk her to imagine what a football/netball/swimming ( pick a sport she knows something about) team would be like if one member was deliberately tripping up the others. She needs to be good team member.
Explain to her what she can do when other siblings are annoying (ignore or talk sensibly to you/dp about it). If there are some reasonable complaints from her about behaviour from siblings that get to her, agree that you will stop ds/dd from doing x or y ( but only a couple of the most reasonable of these - don't make a rod for your own back).
Don't accept over the top stroppy shouty responses. Keep saying "talk calmly and I will listen". Try and keep your voice calm too!
Then talk to her about being grown up and acknowledge she is older and more grown up that ds/dd. She needs to show more grown-up behaviour. In return you will allow her to stay up later. If possible agree a short mum/dd2 one-to-one time for a time in the next week. It might just be half an hour hot choc and chat when others have gone to bed, or varnishing her nails for her on a Friday night after others have gone to bed, or whatever.
I know it is hard to give more attention when you are sooo tired, but think of it this way: You are already giving her a lot of attention for her bad behaviour. If giving her some positive attention will help, then you could end up with a better behaved dd and expending less energy overall!
Is there anyone/grandparent/aunt who could take her out somewhere for a couple of hours ( even just for a walk) while you have a bit of rest and respite?
If this sound too bossy, please ignore. I don't mean to be but am aware my inner teacher can get a bit loud at times!!