At 2 your daughter is learning how to express her feelings. I see aggressive as too strong a word, unless she frequently hurts without provocation as seen from her view. She doesn't have a good enough command of language to use her language. She has no knowledge of social expectations. She doesn't know how to control her body's reaction to anger. Therefore I believe time outs or any other sort of punishment/discipline is not effective. This is a teaching opportunity.
Having her fix or acknowledge that she's hurt someone is the way to go. Having her draw a picture is great if she's willing to do it.
After she's hit someone because they both want to play with the same toy, for example, sympathize with the one that she's hit and give your daughter the words to say. I think you're angry because you want to play with that toy. Give the "injured" one a hug and ask your daughter to say she's sorry. Then move her away from that place and get her started playing with something else.
She may protest but follow thru any way. One reason that I think time outs don't work is that her body is energized by her anger. How can she sit still?
One thing that I do with my grandkids is that when I see trouble brewing I intervene before it gets to the hitting stage. A 2 year old is very impulsive and you probably won't be able to do this often but when you can it gives you an opportunity to show her how to handle wanting to play with the same toy.
Going along with this is being aware when children are tired, hungry,or in general cranky and separate them to play by themselves.
Another thing that I do is to intervene and then have the angry kid run across the room and back so that they get that energy out. I make it a game if they're not wanting to run by saying I'll beat you there and back. They usually start running and I just stand and smile. Usually everything is forgotten for that incident.
It sounds like her karate class is an example of how to divert her attention and get her to run off that angry energy.
Did the 8 and 4 year olds not go thru this phase? Or are you saying that your daughter is angrier and hitting harder or more often?