Our DD's palate is so sensitive, she can tell when food has been contaminated, and will make you sick. Don't ask me how she does it, and she couldn't tell you, either. She has had this ability since she was a toddler. I'd usually order something both of us would enjoy and share with her, and she'd refuse to eat something that I knew was a favorite. Later that day, I'd have a mild case of food poisoning. This situation has played out too many times to be explained as coincidence.
So yeah... take this sensitivity, and food can be an issue. When she was a baby, she'd eat anything (DW was in cooking school - yeah, that's where DD gets it - and DD would greet her at the door with a fervent "Momma! Num-nummm!"), but then she hit a phase around three where she became very selective, and unwilling to try new things. Luckily, she'd already been exposed to a good variety, so it wasn't nearly as bad as my neighbor's kid, who only eats hot dogs and pizza. But even if it was something she liked, but just different from usual, she didn't want to eat it. For example, DW flavors her rice pilaf with chicken stock, and DD loved rice pilaf, but one day she didn't have any stock, made it without, and DD took only one bite.
Medicine was an absolute nightmare. There was absolutely nothing we would have been able to do from an authoritative perspective to make that medicine go down, because there was nothing going on there that she had any control over. It was all about that sensitivity. She could make herself so upset over the flavor of medicine that she's throw it right back up. It was only by helping her calm herself down, and giving her methods to immediately eliminate the taste from her mouth, that she was able to take any at all... and even then, it was a long ordeal.
So that's my experience. Based on that, we would never eliminate choice for my DD at the dining table. If we did, my DD would stop eating enough at meals, she would then be hungry and start wolfing down junk food at every opportunity, and generally be underweight and unhealthy. In other words, all the things you've reported here, I would expect to see in my DD. It's not a disobedience thing, it's a physical/psychological thing. If we serve DD something she doesn't like, she will be physically "grossed out," and be unable to finish, no matter what we say or do.
And so... choice. We consider DD's palate when we plan out our meals, and incorporate things we know she'll eat, but there are some things we eat regularly that she won't. We plan those in anyway. DD always has a choice to join us in whatever we're eating... and these days, we've gotten her to the point where she'll at least try something new, and that's all we ask of her. If she takes one taste, and decides she doesn't like it, good for her, at least she tried it. If she doesn't want what we're having, she can have anything else she likes, provided it's quick to prepare, because we're not a restaurant.
Yeah, she gets more processed foods and preservatives this way than we'd really like, but she's getting all the nutrition and calories she needs in the process, and slowly over time, her palate is expanding to a healthier state.
