i can relate to your granddaughter. when i was younger, the thought of having to taste new foods made me retch. i gagged when forced to eat cooked veggies. once my grandma made me taste a mushroom, and i promptly puked all over the table.
i am much better, but to this day i will not taste something if i think i will not like it. i just can't bring myself to do it. any attempts to force me to eat things when younger just backfired, and i think that is partly why i still so firmly refuse to eat some things. i suggest you do what the previous poster said about hiding veggie purees in food- that does work with me. and just keep offering healthy options or variations that she does like. for example, if she likes raw carrots, allow that to be an option as an alternative to whatever veggie the family is eating.
by the way, i turned out OK. i still don't eat any cooked veggies, but my diet has expanded. i do admit that i mostly eat meat and carbs. my fruit intake is limited as well. still, i am very healthy, with low cholesterol and low triglycerides. my bloodwork and general health is great. the key is to let her eat the healthy things she does like and just keep offering everything else casually.
Many times a child will become more picky as they get older. I like the above statement of using the book Deceptively Delicious. That would be a great way to make sure that the child gets the right amount of nutrients. Even if she refuses to eat the food, put it on her plate anyways. Eventually she will start eating it. It's just that it is new and it may not look normal or good in her eyes.
My son became a very picky eater as he got older! You can't force foods down their throats--- although sometimes I would like to! I puree a ton of different veggies and hide them in his food right now.... or get that book Deceptively Delicious it will help so that your daughter can get her child to eat better.
I refused to eat any sort of veggie until I was almost 20! I couldn't stand the sight of them... they made me want to puke. Children's sense of taste is really heightened when it comes to bitter things- that is why it is harder to get them to eat their veggies.