My husband went through this with our daughter. The reason I say he went through it is because she seemed to act out in front of him and now we know it was to get his attention. He was a yeller and would yell and make threats that he never followed through on. Of course kids can quickly learn that yelling and threats are not big deals. Don't get me wrong, it wasn't all like that. It just seemed when she didn't get enough attention, that's what happened.
My husband first had to stop yelling. It didn't do any good and only stressed everyone out. My daughter is a drama queen so she became more dramatic when he yelled. Well, he's kind of dramatic too, lol. Anyway, that calmed everything down a lot.
Second, we had to figure out what consequences really got to her. Timeouts just didn't seem to work with her. There were times I would put her in timeout and I'd hear her singing! So I found that losing something works. I can put her purse on top of the fridge for an hour and that works. Or she'll lose computer time. I use timeouts if it's something like fighting with her brother. Sometimes she needs to get away by herself because she's mad. My son would rather me do anything but timeouts. He even turned his bottom to me one day because he'd rather get a spanking than timeout. So timeouts really work with him : )
I have also found that positive reinforcement goes such a long way with her. If we focus on the bad with her, the bad gets worse. If we focus on the good, the good gets so much better.
So when she does something she knows she shouldn't do, say hitting her brother. I'll swat her bottom or put her purse on top of the fridge for awhile. I don't yell or get mad. I just talk to her calmly and ask her why she's in trouble. I have her apologize to her brother (and vice versa if he's doing it too). I give out the consequence and quickly move on. When I see the two of them playing together nicely or doing something nice for each other, I do make a big deal about that. So they get consequences. Kids need to know there's consequences to their actions whether it's good or bad. I just try to focus more on the good.
With your daughter, she's pretty young. When she does something to her baby brother, I would talk calmly to her about it. Maybe have her give him a hug and smile big and make a big deal about it. Let her know that pushing is not what you're supposed to do. When she does it again, put her in timeout. With that age I would only let it be 1 or 2 minutes. Use a timer if needed.
Also, could the two of you get some time by yourself? Even if it's just the two of you coloring or something while somebody else watches the baby. I'm sure that would help too.
L.