First, I want to say that I am by no means a professional and probably the best place to start is with her pediatrician. But, with 3 kiddos and a variety of our own frustrating experiences I will offer this: Sounds like maybe she is not able to get her frustrations out in a more appropriate way. Lashing out is often more immediately gratifying for them, especially when they are younger. She really only has her physical being and her voice to use to express her emotions at this age. I think that often when they are this little, words take a lot more effort when their emotions are high so they resort to physical acts.
Hang in there 
. Two year old are all about control. They want it and will do what ever they can to obtain it. It's your job to not let her succeed. totally normal,and I agree with this 100% your dd is obviously old enough to understand you- if her behavior gets her no reaction,and a boring 2 minutes in a chair,it won't take long to stop.A lot of 2 year olds hit. It's not ok and it's something you have to stop but it's not, it and of it's self, a sign of abnormal behavior.
Choose whatever method you are comfortable will and be consistent 100% of the time and you should be able to stop the behavior.
I recommend this one. If she hits, scratches, or whatever, pick her up and look her in the eyes. Simply say, " no....that hurts." Nothing else. Take her to a designated place and tell her she has to stay here 2 minutes. Now, you might have to put her back there 50 times in that 2 minutes, but you do it calmly and without saying another word. When she has SIT for 2 minutes. Calmly tell her that hurting other people is not ok. Let her get up and go about her play. You may do this many times before it stops but if you are consistent it should stop.
Good luck...that is a hard age.
I'm so sorry that you're going through this....our kiddos can be so challenging.First, I want to say that I am by no means a professional and probably the best place to start is with her pediatrician. But, with 3 kiddos and a variety of our own frustrating experiences I will offer this: Sounds like maybe she is not able to get her frustrations out in a more appropriate way. Lashing out is often more immediately gratifying for them, especially when they are younger. She really only has her physical being and her voice to use to express her emotions at this age. I think that often when they are this little, words take a lot more effort when their emotions are high so they resort to physical acts.
Every child is so unique that I can't offer much more than support and aHang in there
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One of the main things that I remember from the book is to focus on the behavior and do not respond to anything inflammatory that they may say.
Thank you so much everyone!!
We try and are consistent but the behavior some days is worse than others. She's a smart kid with an over developed sense of sarcasm. When asked to apologize to me she'll sometimes say sorry in a real fake way with a smile on her face. I just hope it's a phase. I hope to have a really good relationship and bond with her but she's a total daddy's girl. If he gets up with her in the morning and I wake up a little later she gets upset if I so much as say good morning to her - and will tattle on me to my DH for speaking to her. It's a real power struggle for his attention I'm guessing. He works from home in a home studio and I think that might have a lot to do with things. I'm with her more, I discipline more, he's more 'fun' so she knows that he'll pop his head in if he hears her having poor behavior. it's exactly what she wants - to see dad 24/7.
Keep any advice coming! We use a montessori approach which I love, but still find myself having moments of pure frustration sometimes.
I really appreciate all the advice and words of encouragement. People say how hard raising kids is and man, they didn't say the half of it.

When asked to apologize to me she'll sometimes say sorry in a real fake way with a smile on her face. I just hope it's a phase. I hope to have a really good relationship and bond with her but she's a total daddy's girl. If he gets up with her in the morning and I wake up a little later she gets upset if I so much as say good morning to her -
I really appreciate all the advice and words of encouragement. People say how hard raising kids is and man, they didn't say the half of it.
She started around 18 months just before her vocabulary "explosion" but the terribly undesirable behavior persisted. To our dismay, I found that despite my consentrated efforts at consistency, a lot of the traditional sorts of advice did not work. They actually seemed to make her worse. 
the reality was he was very intelligent,wanted to keep up with big bro,and lacked the physical ability to do it. He was a frustrated toddler,and boy he let us know!
we had no choice, he saw things as black and white, no grey.