So hard. My DCs are the same age and DS can be really trying. He's been kicking me recently which is particularly painful! For the past two months, I've been trying different things because I was at the brink of despair every day!
I take away his LazyTown poster every time he misbehaves - with an explanation. Is there anything you could take away from your DD and that she can earn back with good behaviour.
If he howls, shouts and screams, I tell him I won't talk to him until he talks normally.
I agree with others who say keep calm. I feel like I could blow up sometimes but I really really try to keep calm because otherwise it escalates and he gets even more upset/defiant/angry (whatever mood he's in).
Plus I always feel a whole lot better about myself if I've managed to stay calm. I force myself to ruffle his hair and say, "When you feel better and can talk normally, then come and see me and we'll have a hug," Then it's not me versus him anymore. It's him versus him and that can't last for too long.
One other thing I think of that seems to help me is that I imagine he's a child who is being fostered. Now, that sounds really weird I know but it takes me away from the, "You're so ungrateful when you have so much and we do so much for you." Instead, I just think, "Poor lad. He'll come round,"