I have 3 intense children! Now that they're a bit older (10, 8, 5) their intensities have taken different directions, but I completely hear you!! I've been through most of what you described, and with more than one child.
The first thing is that she is needing limits. Yes, she's fighting you on them all the time, but she is also craving them. That is one reason why she is going back and forth so much on her decisions. She needs help to make choices. Don't give her a choice where there isn't really one (ie to stay in the car - just take her out, or to get dressed or to take a bath). Instead, give her a choice of whether she will climb out of the car herself or have you take her out, whether she wants to blue or the green shirt, whether to take a bubble bath or a shower. The point is to give her two choices where you are ok with either choice. She gets a sense of control without feeling out of control (like no boundaries can do) and you still get to have things done within your limits. Her going back and forth could also be a way of testing you (will mommy still love me if...? or how far can I go before mommy gets angry? - not necessarily on a conscious level) Or she may be indecisive. When she picks something, stick with it. If she asks for yogurt, serve it for her. If she changes her mind, she doesn't have to eat it, but don't fall into her game by putting it away and getting it out over and over.
Now here's the trick - look for the positive in all of this. My daughter (my oldest) was VERY determined and wouldn't give in. I just kept telling myself this would be a good trait when she got hit with the peer pressure (and it has been helpful). My son (middle) has and is always in his own world, playing out some imaginary space battle or something in his mind - but he may be the next George Lucas or Gene Roddenberry. And he's very sweet and cuddly and always tells me he loves me. My youngest was very clingy and never wanted to be put down, but he's developed a security that allows him a lot of independence. There have been fights and tears and a lot of frustration while they're growing up. But I can see now that they are all VERY bright children and I would guess that your daughter is too - my experience has been that the very bright kids are often also very difficult; maybe their brain is going too fast for their emotions or decisions or whatever to keep up!
As far as diet, I have heard stories about red #40 since I was little. My mom swears that it was a big factor in my brother's ADHD (not causing it, but making it harder for him to deal with) but there is no scientific evidence. Go ahead and avoid red food dies and other artificial stuff if possible, but don't go overboard. In general, a well balanced diet with plent of whole grains and fruits and veggies, low on fat and refined sugars, is good for everyone. She will feel better if she is getting good nutrition and it may help her behavior too.
If the doctor isn't taking you seriously, you may want to find another doctor. A pediatrician should be able to help counsel parents through difficult behaviors and listen to parents concern. Even if he feels like its nothing, he should listen and work with you. My kids' pediatrician has always told me to listen to my gut - that mother's intuition can clue me in to something going on. Also make sure that you are listening to what the doctor is saying if he's trying to help deal with behavior. He's probably not saying you're a bad mom for struggling with these issues, but trying to help figure out what to do. Most behavioral challenges aren't going to be solved by a simple diet change or pill (I wish it was that easy! <VBG>)
I know I've rambled on a lot. If anything isn't clear or you have more questions, feel free to contact me directly. Just know that you aren't alone! There are moms out there going through the same struggles, and you can make it through!