Physical actions are a way for your two year old to communicate. Teach her to use her words and say NO! instead. I know it seems like you are teaching her to talk back to you, but it is allowing her to express her feelings in an acceptable way. When she says no, you can tell her you understand her feelings and "it will be okay" even if she doesn't get her way. It's not her turn now, maybe next time. When she does get her way, make a big deal about it so she sees that she gets turns and can learn to take turns with a good attitude. This (no surprise) comes with age and experience. Give her plenty of turns to speed up the process.
Another little trick is to hug her and reassure her it will be okay. You see she is upset, and it will be okay. She will probably collapse in relief because she feels out of control and will be relieved that "it will be okay" It depends on her personality, but it is all about communication! She is trying to communicate so make sure you tell her that you HEAR her and she is important, even if she doesn't get her way, she is heard and important. She doesn't need to hit for you to hear her. Be sure to give her turns, ask her what she wants to do sometimes and remind her of the times she didnt get her way, and tell her now it's her turn. Tell her when she will get a turn if it's not now. This can help her realize she gets turns and not be so upset when it's your turn. Ask her if she wants you to hit and bite her when she plays at the playground? What would that be like? Maybe show her so she can see what her behavior looks like and decide she doesn't like it. (not really biting and hitting but acting like her she can feel and see the behavior from your perspective), it's a good teaching technique to mirror your child's actions so they decide they don't like it)
Good luck!
B.
www.twominutemom.com