How long would your daughter go without food if you don't give her exactly what she wants? Normally I wouldn't say something like this, but she needs to find ways to get past her intial revulsion if the food itself isn't harming her in some way.

I HATE califlower and brocolli (texture, smell, and taste), but it took me having food allergies to many other foods and those two being "safe" foods for me to voluntarily eat them again. I still reserve the right to make funny faces and rude commentary about either food while attempting to force myself to eat them (I am 33). It would cause me more long term harm (certain vitamins missing from my diet) to not eat them than to eat them due to my very restricted diet.