I think I know what her problems was. To illustrate, I will quote from "Wee Free men" by Terry Pratchett (one of my favourite authors). It's one of his books for children although I find ALL his books eminently readable by anyone of any age with a good brain.
Setting the scene - Wentworth is a small boy who has been kidnapped by the Queen of the Fairies, who thinks she is good with children but isn't really. To keep Wentworth happy, the Queen has given him all the sweets he wants. And Tiffany, Wentworth's 9 year old sister who has gone into Fairyland to rescue her brother, knows why this is the wrong thing to do.
"Wentworth was sitting on a large flat stone surrounded by sweets. many of them were bigger than he was. Smaller ones were in piles, large ones lay like logs. And they were in every colour sweets can be, such as Not-Really-Raspberry Red, Fake-Lemon Yellow, Curiously-Chemical Orange, Some-Kind-Of-Acidy Green and Who-Knows-What Blue.
Tears were falling off his chin in blobs. Since they were landing amongst the sweets, serious stickiness was already taking place.
Wentworth howled... He only stopped crying when it was time to breathe in or die, and even then it was only for one huge sucking moment before the howl came back again.
Tiffany knew what the problem was immediately. She'd seen it before at birthday parties. her brother was suffering from tragic sweet deprivation. Yes, he was surrounded by sweets. But the moment he took any sweet at all, said his sugar-addled brain, that meant he was not taking all the rest. And there were so many sweets he'd never be able to eat them all. It was too much to cope with. The only solution was to burst into tears.
The only solution at home was to put a bucket over his head until he calmed down, and take almost all the sweets away. He could deal with a few handfuls at a time."
I do think she may have a version of this problem, coupled with extreme anxiety and the intense egocentricity that we usually only associate with very young children. You eating something different, isa reminder tat her decision to choose something else is locked in and irrevocable.
One way that MIGHT work, is for you to swap tastes. It needs to be mutually agreed on. It's something that a lot of married couples do when eatingout. husband & I do it often - we've each ordered what we want but it all looks delicious, choosing was hard. So he orders the veal, I order the lobster, and he gives me a taste of the veal while I give him a taste of the lobster. And again with dessert - I order the chocolate mousse, he orders the sticky date pudding. My mousse is served cold with cream, his is served hot with custard. We each have a small taste of the other's. Sometimes we feel that we made a bad choice, I might like his pudding better than my mousse. But generally, it confirms that we're happy with the choice we made. And if we're not - we now have had tastes of both, so we haven't completely missed out.
easy child was a problem like this. She had to have what she considered a fair share of everything we served. even if she wasn't home for that meal - if I cooked a roast dinner and made a special pudding for dessert on a night when she was staying overnight at a friend's place (and probably eating out somewhere fancy) she would be very upset to get home and find that we had nothing left, we'd "eaten her share".
If we were eating out of a communal supply (such as one giant pizza, or one huge pile of hot chips (fries) then she would be wolfing them down so fast to make sure she got at least her share, that the rest of us would struggle to keep up.
Maybe what she needs, is to have a chance to at least taste all options, then make her choice. Once she knows what it tastes like, she can't whine about missing out because choosing an alternative is HER choice.
What I had to get easy child away from, was the thinking that she had to make sure she wasn't being left short in any way. Because she linked her neediness to food, she now has a huge weight problem.
I've seen something similar in another young girl I know, a bit younger than difficult child 3 - I had to take this girl with others in my after-school class, on excursions where afternoon tea was provided. She would HAVE to take a sample of everything, often to the point of seeming a glutton of being rude, bargaining with other kids if they took the last biscuit or whatever. Since the variety was always greater than the number of serves, this made our entire group look bad. I would have to almost literally drag this girl away from the food and sit on her to stop her from sneaking back and getting more. This in an otherwise easy child kid. I could never make this kid understand, that providing ten different kinds of biscuits did NOT entitle her or anyone to take one of each kind (ie 10 biscuits). The variety was there because some people preferred one kind of bisucits, other people preferred different ones. NOT to allow ANYONE to binge and taste everything. The allowance was TWO biscuits, not ten.
Finding out why the child has this mindset, and how to resolve it, is somethingh I should have done with easy child and now wish I had addressed with my student, by talking to her mother. The girl still is a problem, desperately wanting attention and friends even though if she just relaxed a bit she would realise she is a really great person in her own right. But she's now mixing with a bad crowd because she is so vulnerable and so desperate to be liked, that the bad crowd can get her to do some really bad things.
Very sad.
I hope you can find some way around this for your daughter - you might need to get creative.
Marg