You just described me as a child! I've yet to meet anyone who is a pickier eater than I am (they don't exist!), and it's a tough thing to tackle. My dad always thought that I was just being stubborn and dramatic about not liking a lot of foods, so his rule was if I didn't like what was made for dinner, I didn't eat. There was no special exception for me. Forcing that rule, while somewhat reasonable if I were just being stubborn, didn't help anything: It taught me to be anorexic as a teenager, and as an adult, I overindulge in what I do like because I'm the one who buys the food and makes dinner now. (Just my experience; I'm not insinuating your family is like that.)
To this day, the only fruit I eat is apples, and I don't eat any veggies. My best suggestion would be to try sticking with crisp and crunchy fruits and veggies for her, though. Those seem to prompt the fewest gag reflexes as far as textures. Mushy stuff is harder to handle when you have a sensitivity to textures.
Trust me, it will be embarrassing for her later in life when she stays with friends and doesn't like what's made, when it comes to going out for dinner, things like that. I dread any of the above because the small amount that I do like is rarely served outside of my house. That's punishment enough for something we don't control.
You have a good plan set out for your goals, and you are right not to allow anyone to make you feel like you are not doing right by her. Make sure you aren't blaming yourself either. Just keep providing any healthy foods that she does like, have her help in setting a weekly menu for the family, and give her a daily kids vitamin if you are worried that she might not be getting all that she needs from what she eats. Let her experiment, helping to prepare foods in ways she thinks she might like them. While she may not grow into an adult who eats the recommended daily values of all food groups every day, she will start finding new things here and there that she likes.
Luckily, it's not necessarily an inherited thing, either. Out of my 4 kids, only one of them can still be considered a picky eater. The other three are what I lovingly refer to as my human garbage disposals: they'll eat pretty much anything you put in front of them every time. They wouldn't turn down junk food for anything, so I just watch what we buy at the store, and they have no arguments with eating healthy food. I feel pretty lucky to not have a bunch of mini-me's!