If they were being violent, I wrapped and tucked. Arms round their body, legs round their legs, head tucked into their back so they couldn't headbut me! And I held onto them until they gave up (this can take a while!)
If they were just tantruming, I made sure there was nothing they could hurt themselves with, and I left them to it and went to do something else.
Sometimes I lean over them and tell them they are not doing it right, "No, you need to kick your legs, kick higher, roll over, yell IT'S NOT FAAAAAAAAAAAIR, shake your arms..." But only when I'm bored
I used to make wa-wa- noises by wibbling their lips, or pressing my hand repeatedly over their mouth. Again - I plead boredom
Sometimes I joined in. Or started singing.
Sometimes after they were done, I clapped.
You'd be surprised though, how little they tantrum these days. Compared to how they USED to be - well, ds1 used to be, it's loads better! ds2 has always been more laid back (although he has started trying to tantrum, but he's really not very good at it! I tend to go with leaning over him and giving him directions these days!!)
I think what worked for me was I stopped caring. I mean, I made sure they couldn't hurt anyone, but beyond that, I just stopped giving a crap.
And of course, you NEVER allow them to gain anything from the tantrum! Rule no1 - don't give in!
It sounds like something is going on with her - do you have to give a lot of attention to your other child (understandably) if she sees this behaviour being 'rewarded' (I know it's not a reward, but she won't) then she is more likely to copy it. Also, if her older sister is behaving in this way, well, she is the model isn't she? To your dd2, this is how you behave and you telling her it is not, is not as powerful a message as what she sees.
Perhaps in order to deal with dd2, you need to focus on how you deal with dd1, if that makes any sense?