Dear Elizabeth,
Two things stand out. First, there are indications that, while your daughter's behavior is problematic, her emotional state may be a cause for worry. Because of this, I'd suggest you seek a pediatric mental health evaluation. This can address the possibility of mood disorder (versus, for example, a sensitive personality without underlying mood disorder), and help design a systematic approach to the behavior.
Second, it's important for you and your husband to maintain your equanimity. Sometimes it seems to us parents as if we must automatically be angry in response to our children's behavior. But whether to be angry or not is actually a choice. And sometimes we choose to be angry, or let ourselves become angry, when the better choice would be to maintain our equanimity while, at the same time, we set firm limits and follow through in a decsive way. Children's misbehavior needs to be addressed in a resolute way, but it does not always have to be accompanied by parental anger. Dr. KDK
Have her tested to see if she is depressed, has a sensory integration disorder, etc. This is crutial. She is not doing this on purpose and cannot control herself so punishments, yelling, getting angry at her will not work but make things worse. Kids with disorders already have low self esteem, and anger and negativity from parents will do nothing to help her.
How you react to her will set the tone for your home life. Don't overreact to things and stay calm and detached. Give her lots of love and specific positive praise for good behavior. A good book is "The Defiant Child" by Dr. Douglas Riley.
But getting an accurate diagnosis is critical.
You may want to try eliminating artifical dyes, flavors and preservatives from her diet. Cook from scratch and use no preprocessed food. Limit juices, sodas, sugar, and anything with corn syrup. Try reading "Is This Your Child" by Dr. Doris Rapp. A good site on diet and behavior is foodallergy.org.