My dd's (nearly 6 and 9) can be so VILE to each other

[DukesOfTripHazard]

They never miss an opportunity to wind each other up:

DD1 (taunting)'Oh, look, your friend's handwriting is really lovely'.
DD2 'Waaaah! You don't like my handwriting! (hits dd1)
DD1'You little brat!' (pinches dd2)
DD2: 'Ow! You're fat!' (thump)

Why do they do this? How can I encourage them to stop? I am shouting A LOT at the moment. Really a lot and I am on edge whenever they're together. I know I need to chill out and not react... and I'm working on it. But are there other things I can do? Books? I like books.

How can I help them like each other more of the time?

I think this is fairly normal. I remember my mom talking to me and my sibs a lot about siblings looking out for each other and being kind to each other when we weren't fighting. Think she ignored that kind of exchange and only got involved if there was something awful going on. Punishment usually took the form of doing something nice for the wronged party. If it got really bad, she'd separate us--just send us to play in different rooms or give each of us tasks in different parts of the house.

FWIW my sibs and I are pretty good friends now so some of her tricks must have worked!!