N.,
I HATED vegetables as a kid. I was your classic stubborn, picky eater.(Yes, I have apologized to my mother more than once about this since I now have kdis!) My mom tended to overcook the veggies and served them mixed in with other things and I didn't know what I was eating. I became a pro at mining out every onion fleck or mushroom bit.I had a very sensitive stomach and very acute sense of taste. I have gagged on more than one occassion when being force-fed stuffed cabbage, peas soup, etc....It was traumatizing to me. I didn't feel like I was being willfull. I felt that the adults had no idea what horrible thing they were asking me to do by eating certain things. It would be like me offering them worms and saying, here eat this it's good for you!
You should try offering/serving more raw veggies: lettuce, spinach, carrots, cucumbers, red peppers, tomatoes, peas (shell, snow, and snap), celery and other sweet veggies. Let her eat tons of fresh, raw fruit, too. It is all good for her. For snacks, have a variety of nuts, raw veg or fruit, raisins, cheese, etc. Raw diets are one of the healthiest. I think kids intuitively know this, but can't articulate it. If you have a farmers market nearby shop there. Local, fresher food tastes way better. In fact I didn't really start to like veggies until I was 20 something and grew my own. sounds like you don't have time to garden but if you could at least plant some peas, you'll be amazed athow much she'll eat.
Try to cut back on the processed stuff. Try a month of no hot dogs, etc. If she gets hungry enough and there are no other options, she might be willing to expand her horizons. Also, let her help you cook so she can see what goes in the meal. Let her snack on the components as you are making it so she can taste that they are okay.
It doesn't sound so much like a power struggle as much as she has very acute senses and perhaps some textural sensitiviy.