When our kids were small, one of the things that drove me crazy at theme parks (or frankly any vacation) was the constant begging for treats. We could be on our way to lunch and they would be distracted by all of the options for sweets and snacks along the way. It wasn't a matter of hunger, but of the appeal of the junk food. Not only did the cost add up, but of course it would ruin their appetite for the actual meals where I wanted them to get a bit of nutrition, and often resulted in a lot of wasted food.
What my husband and I decided in response was on vacation we would have "snack time" at a dedicated time each day, usually 3pm. We explained to our kids that at that time they could choose whatever snack they wanted. So anything they saw before that, they would file away as a possibility. Instead of saying no or responding to whining, we got to respond positively: "That looks yummy! It would be a fun idea for your snack time treat." The kids got on board with this very quickly, to the extent that at ages 17 and 19 they still plan their own days this way when vacationing, "At snack time, I'm going to come back here and get that funnel cake."
We don't budget too hard on meals themselves, but we do ask our kids to only order what they will eat, and we as a family do consider when sharing items will make us happy. And as the kids have gotten bigger, we've also adopted the practice that if anyone doesn't want dessert at dinner, they can choose an evening snack later when they're hungrier (that we'll pay for). If our kids want to junk it up beyond that at this age, they have their own money from their part-time jobs, so they can buy themselves as many Mickey Bars as they like if they really want -- but they seldom do.