Severe behavior problems in 4 year old daughter

My 4 year old's behavior has slowly gotten worse the past 2 years. My daughter will never, ever will do what she is told to do. Not for my husband, or myself. (Not even for a gymnastics coach, which is an activity that she LOVED to do.) I feel like 80% of the day I spend dealing with her crying, screaming and throwing a tantrum. Even the slightest thing that upsets her, like her being told to pick up her toys, she will throw a fit about for as long as an hour or so. Any punishment (or just a command she doesn't like) results in the never ending tantrums (time outs, early bed time, taking a toy away).
It truly scares me. Many times I feel like she absolutely has no control over her actions. She will be dying for a toy or reward I promised to her with if she behaved well, and she still behaves horribly. And she is devastated when she doesn't get her reward.(Like she tried so hard to be good!) Sometimes when I can get her to finally calm down, she says she understands why she had a punishment. But the same actions erupt again shortly after.
I try my best to avoid public outings, but it's not always possible. For instance, at the grocery store, she cannot sit still, or keep from screaming. As soon as we get to the grocery store, she knows automatically she has to sit in the cart, (She won't hold my hand and walk with me. If I even try, she ends up hopping, running or just plopping down on the floor, refusing to walk at all. It's very entertaining to her, she laughs and thinks it's funny.) but she fights, and kicks and screams and makes it impossible to sit her in the cart. By the time I have finally gotten her into the cart, she spends the entire trip screaming. Dining out, she is coloring a picture and fine one minute, then out of nowhere she just explodes over nothing! ( A crayon broke, she needs to use the bathroom, etc.)
I can't take anymore. It's past disrupting our lives. I'm heartbroken to be spending her childhood like this together. All/any suggestions please!

[Kevin Kennedy, Ph.D.]

It's time you arranged an evaluation with a child psychiatrist. The description you offer extends far beyond what can be regarded as norma-spectrum childhood behavior problems. If you don't know where to turn for such an evaluation, ask her pediatrican for a recommendation. If that fails, call her insurance company and ask for a list of psychiatrists in your area.