My main problem now is the dishes, she won't let me do it, she pushes me away from the sink screaming 
, it sometimes take 5 to 10 min (which is very long to ignore) before she finds something else to do.
I have to sing myself (even if very badly). Did that with DD1 too. "I aaam cuuuting the carrroooootts now.....soon it will be tiiiime for the pepppperrrsss" when I ran out of nursery rhymes 
or even "you are driving me crazy with your screaming there is nothing you can do, I am not letting you climb out of the window...." IYSWIM.
DD2 is very good out though, she loves it, chat with people, she keeps the screaming for me at home.
Is yours starting to talk? Is she completely mobile?
DD2 is very tall and very physically developed (think 2 yo ability), and that has helped the tantrums, because she can do almost anything she wants (mainly follow her sister everywhere and reach anything in the house).
She is starting to understand and make herself understood too, which has also helped. Still a bit to go.
Make sure your eldest are not winding her up behind your back too. She is still a baby and don't which toys are which, and so on, but if they push, snap, run away, scream that what she will learn to do. You can see I spend some time trying to educate DD1 (6) 
it is getting there too. She has finally understood that if she screams when DD2 screams, it just make it worse. And she now swaps precious toys instead of snapping them away...