10 yo DD is bright, friendly, articulate, outgoing, confident, does pretty well at school, invovled in several extra-curricular activities, has plenty of friends, etc, etc. Teachers, coaches, friends' parents all say 'she's so lovely, so mature, so helpful, so polite, an angel' blah blah blah blah blah.
Except at home I swear to god, she is like the psycho child from the exorcist whos head spins round and vomits green goo!!! 
- I ask her to stop making some bizarre annoying noise and she immediately repeats it over and over and does not stop until I shout
- I ask her to eat breakfast, she insists she's not hungry. Except as soon as it's time to leave for school she is suddenly starving and starts screaming that i'm the worst mother in the world for not allowing her any breakfast.
-I ask her to stop making horrible faces at her brother in the car rearview mirror (she's in the front, he's in the back). She looks me in the eye and tells me she's not (she knows I can see her). I tell her to close the mirror. She insists she has to do her hair now, it's urgent. I tell her to close the mirror. She refuses. I tell her she's punished. She screams how unfair it is that I am punishing her just because she wants to do her hair!
-Kids are at table eating, I am next door in kitchen (no room for table in kitchen). She says DS is making faces at her. Try giving her the benefit of teh doubt so tell DS he has to come eat breakfast standing in the kitchen where i can see him. She follows and stands exactly where he is, leaning over him, claiming she's 'just putting her cup down'. Tell her just to move over. She starts saying its not her fault he's annoying her, he's an idiot, he kicked her (again, I can SEE them and he has NOT kicked her). Tell her to cut it out or she will be punished. She starts screaming at the unfariness. I point out she is not punished yet, she still has the chance to chill out and all will be fine. But she is either physically incapable of chilling out/calming herself down (having gotten herslef worked up over nothing in the first place) or can not process what I'm saying becuase she keeps screaming until i too am screaming and then she is punished.
I could go on and on - I say have a shower, she says no. I say ok don't have a shower, go to bed. She says but I HAVE TO HAVE A SHOWER! I am literally tearing my hair out. We have tried everything. WE have tried having heart-to-heart talks when she and I are both calm. Her dad has tried having hear-to-heart talks. We have tried using mobile phone, treats, late bedtime as incentive. At the moment we are working on a 2 strikes and your out (which she says she doesn't have to abide by because she didn't agree to it). She gets 2 strikes a week. The first time she just gets sent to her room for a short period of time or an early bed time. the second time she loses her favourite extra-curricular activity which seriously upsets her but at this rate she's never going to go back to it again!
DH and I are actually at the point where we are considering having her speak to someone becasue we really don't know what else to do.
Sorry, I didn't mean this to be so long.
Often my DD is a major PITA, as am I 
BTW when coming down with something. And those few days before the symptoms have shown up are usually the worst!