Find a good psychologist/ therapyst. From what you are saying, this isn't all about your daughter. This has something to do with the relationship the two of you have.
That said, it sounds like you need help today ...
I looked at your post again, and found four specific things:
1. hitting brother
2. calling names
3. failure to leave when told to
4. not getting in car
First, I am a bit strict about how my children treat each other because my kids are five years apart and the size means someone could get really hurt. I also have two spirited strong willed, hyper kids, so I have been here. My daugher who is the oldest was barred from the family room becase of hitting her brother, until she could show me appropriate behavior in other settings. She was not allowed in the same room with her brother. This is an important conversation to have privately and when everyone is calm. I took my daughter for ice cream and while we walked home, I asked her what she thinks I would do if someone repeatedly came into our house and hit her. She said that I would stop them. I said you are right. It is my job to keep you safe, because I am the Mom and I love you. Now, I have a job to keep your brother safe too. Then I told her: you are the person coming into my house and hitting my child, and I cannot let you do that. So until you can show me that you can behave you are not allowed in the same room with your brother. Do you understand? So, if your brother is in the family room, may you enter the room? wait for the "no." If your homework is in the family room, with your brother are you allowed to go in and get it? wait for the "no." Tell her this is the rule of the house, until she can show you that she can treat the rest of the family respectfully. If she is anything like my daughter, she try to argue, negotiate and avoid answering the questions. Just keep repeating it, and ignor her remarks (as much as you can) stay focused on the goal of protecting your son. This will take awhile. (If you are afraid she might run away, don't do it outside. You might need a strong guy around since you said you cannot physcially handle her. Plan, think ahead, and do your best to remain calm. It is really hard.)
I did this to my daughter. It took her about a week, but then I had my kids trained by the time they were 2 if I said go to your room, they went. There was no gray area there. It may take your daughter a bit longer, particularly if she is bright.
Next, and I am serious here, call the boys and girls town hotline. These people know how to deal with kids like this. She isn't your only child, and what she is doing is abuseing the rest of the family. You have to think about protecting your other children.
I had a sister like this, turned out she was bipolar, my parents didn't do much, and I still have trouble sleeping at night because of all the nutty stuff that happened in our house. I have had at least one professional tell my I have post tramatic stress syndrom because of all the nonsense.
Lastly, when my son wouldn't leave when it was time to go, and when he refused to get in the car when I said. He didn't get to go. Honest, when my son was two he and I didn't go anyway, except doctor's appointments because I couldn't trust him to leave and get in the car when I said. I went food shopping at night after my husband got home from work. My daughter could come, and when my son begged to come. I (as calmly as possible) told he wasn't allowed because I couldn't trust him to listen to me. When he could demonstrate good listen then he could go, but first he had to demonstrate good listen to my satisfaction. I also purposely schedule a few babysitters (who were in on it) and arranged from the rest of the family to go bowling, mini-golf -- stuff like that. He got left home because I couldn't trust him. He begged and I explained. Being left out is real punishment! I think it took three weeks, and then I gave him another try. From then on, I just tell him: "if I cannot trust you to listen when we are out, I guess you just wont get to come next time." It works like a charm, still, three years later. It was a really rought couple of weeks for me. I hated doing it, but strong willed kids require creative solutions, and they need to know you are in charge! They really do need to know that.
Best of Luck.