The way children learn "Why" they did something is by the words their parents teach them..
When she looks like she is about to lose it, I am sure you recognize it.. You can use the words. Pick the appropriate one.
"I can tell you are frustrated because brother was using the stool when you wanted it."
"You need to find your patience, brother is using the stool."
"Use your nice words to tell brother what you need."
"We do not hit brother, use your words to tell him what you need."
"Take a breath and think of the words to ask brother what you want."
"We do not hit people."
"I know you are embarrassed that you fell, but do not hit brother."
"Go to your room and find your nice words."
"Hitting (scratching, biting) hurt. Go to your room and find your words."
Also EVERY time she hurts her brother, she gets a time out.. She should get 6 minutes. If she argues, gets up from time out too early, return her to time out and the time starts over again. YOU have to enforce these rules. Even if it takes dozens of times for 1 incident..
You also need to spend some time with her talking about feelings. Then another time about feelings. Frustrated, angry, mad, sad, embarrassed, tired.. and what each is and how to handle it when it happens..
This is just as important as learning to read or write.
Yes, it takes time, but it is worth it. YOU need to find the strength to stick with this.