What are her emotional responses like? Does she express appropriate emotion. Can she correctly identify accurately emotions of other? Does she make eye contact? Are ther situations when she relates well to peers or adults?
yes to all of the above - she does not care if you restrict her - we can take away an item she likes, not go somewhere she wants to go, etc. and she will not relent.
Just to clarify -- she DOES have appropriate emotions etc. If so, that pretty much rules out serious disorders. She likely is exhibiting Oppositional Defiant Disorder or early signs of Conduct Disorder. Children at this age are trying to learn about how much POWER they have. They will escalate their behavior because expressing power is more important than any punishment. My first recommendation would be psychological evaluation and consultation to help you develop strategy. One of my favorite references is by Rudolf Driekers, "Child the Challenge" and "A Parent and Teachers Guide to natural and Logical Consequences". They are a bit old, but I haven't found anything I like better. They are available ay Amazon. They are redundant, so just one of them is sufficient.