R.B.
I believe what you are going through is a quest for attention, negative or positive. Sure, she ends up in timeout, but then you spend individual time with her trying to talk about feelings, etc. Behaviors happen for a reason. Something is achieved by her action. Timeout is not unpleasant. She sings and enjoys her timeout. She knows what she is doing is working. It is not that she hates her brother, but she likes something she gets out of it, individual attention from you more than likely. Maybe you could try doing the opposite of what you're doing. Ignore her actions. Do not let her hurt her brother, but don't give her the attention she is looking for. Also, try something positive. If she is sitting nicely and playing near her brother, praise her for being good, for keeping her hands to herself and treating her brother nicely. If she is being mean to her brother, remove the baby from her area, but don't react to her and give her attention.
Catch her being good. She could be having a fit on the floor, kicking and screaming, but she is not kicking her brother or the wall, find something, and praise her for something. It will stop the tantrum and change her mood. I know this sounds kind of crazy, but you've got to get her to start doing positive things for attention. Right now, she figures negative is better than none. She doesn't care if you punish her, because then you will feel kind of guilty and spend some time with her talking about feelings, etc.
If she is starting to be good, tell her that when her brother takes a nap, you will sit and play a game, read a book, something with her, just for her, as a reward for being such a good girl.
I hope this makes sense. Good luck.