My DD is the same way. If she knew she'd get dessert without eating her dinner, she would not eat any dinner. (And then the "sugar crash" would come.)
What we do for her (and I do this at restaurants at home, too) is divide the meal at the beginning into "must eat to get dessert" and the rest. (Sometimes the portions are big.) I usually include the veggies and about half the entree in the "must eat" portion. She's welcome to eat anything else (or not), but she doesn't have to eat the rest to earn dessert. And she knows at the beginning of the meal what's required, so I don't have to hear "how many more bites?" or "is this enough?" throughout the meal.
We usually go through a few days of "how much of this do I have to eat?" when we get home. At home, it's "all of it" because i start with reasonable portions on the plate.
But we are usually more lax on vacation than at home. (At home, if you didn't eat your meal, you wouldn't get dessert *or* a snack later -- unless it was a very healthy snack. On vacation, you wouldn't get dessert, but if we all decide to get Mickey bars later in the day, you'd probably still get one.) I think kids can learn that there are different rules for different situations.