It'll be interesting to read more from parents of several siblings on this one. The advice to look at how you discipline your older son and whether that's working is great advice.
Addressing just consequences -- find her "currency." Obviously she doesn't mind being sent to her room or having time outs; but what WOULD she mind losing? TV time? A scheduled play date? A toy she adores? At a time when she's being calm and not confrontational, sit her down and have a very calm talk about behaviors and your new set of, as someone rightly said, "natural consequences." She does X, she loses Y. Instantly, no fuss, no pleading, no negotiation, no yelling from you, it's gone. You can perhaps give her one warning if you see the undesired behaviors on the horizon, but don't let her get too far into the behaviors before you give her consequences.
Losing a few much-anticipated play dates or having a new game or toy instantly taken away (for a substantial time, not a hour or so), may show her you will follow through. She may say, "Oh, I don't care, it doesn't bother me," but be consistent and if needed find new currency that she will care about. It's important that the consequence follow immediately after the behavior, with a very clear statement from you that "You did X. You made the choice to do this. Now the consequence of your choice is Y."
As for behavior while actually on a play date -- I'd have her instantly apologize when she says "you're not my friend" and remove her if she does it a second time. And if she touches anyone with shoves etc. -- the play date's over, she's in the car in 10 seconds flat. Like another poster said, a few five-minute play dates or park trips and she'll realize you really will pull her away from her fun without hesitation.