Inappropriate is the word I would use for that response.
Whether or not they meant to be funny or rude, when I was Disney trained (years ago, granted, maybe they aren't so specific with CM's anymore) we were told not to ever use sarcasm when speaking with guests or any other language that could possibly be misinterpreted as rude even if it was meant to be humorous. It sounds like this person flunked Guest Relations 101 and needs a refresher. CM's will get in trouble if they upset a guest even if they were trying to be funny.
I feel so sorry for your daughter! I can understand them refusing to let people take anything away in boxes from a buffet, otherwise people (not you, but others in general) would take advantage of the situation. As it is, many people help themselves and take extra food from the buffets out in their purses/etc. for later, which makes it tough on the rest of us, especially those with a special situation like yours.
In sit down restaurants, there is no excuse for them denying that request, if they have 'doggy bags' then they can pack up a meal for one child!
Since one adult has to stay out of the restaurant with the child anyway while the rest eat, I would just plan to skip sit downs with this child until she gets over it. Might not be convenient but if it were my child I'd rather have her eat counter service (maybe eat out in the open, on a bench in the parks) and keep it down than feel sick at a sit down, dinner show or no.
Good luck!