I didn't realize how hard the birth of a new baby would be for our ds1 either. It's a huge transition. Ever since his brother was born, I've been reading and researching all sorts of GD. So I can share with you what we do and what I've found, but I highly recommend one book in particular- Helping Young Children Flourish.
My guess is that your daughter has some pent-up feelings, anger, jealousy, and so forth. It's totally normal, she just needs to release them in a safe environment. Next time she starts acting destructive, or violent, first stop her. Then just hold her and say, "I can't let you do that." Try not to put blame on her, or make her feel guilty. You may not need to say much else, and just listen to her and hold her. At this point she may be screaming and thrashing around, or maybe not. She may start to cry and tantrum. This is good, this is what she needs to release her pent-up feelings. Try not to stop her from crying, just offer love and support, she will stop when she needs to. But don't leave her alone to cry. She needs to know that you are there for her, to listen.
When ds1 gets this way, I see it as a cry for help. He may start yelling, or doing other things to be obnoxious and get our attention, or even be destructive, or violent. I then take him, hold him and say, "You seem to be having a hard time today. I'm just going to hold you for a bit." He may start to squirm, and even laugh, then he'll say, "No! No!" And I respond, "But I can't let you do the things that you are doing, they are disrespectful/hurtful." Then he'll start to cry and tantrum, at this point, if he still wants me to let him go, I will because I know he's not going to hurt anyone or anything. I sit with him, and offer support until he has stopped on his own. After that, he's fine, and very pleasant to be around.