We usually tell our kids they can have one special treat a day (depending on how long we are there). Once they have their treat, they will not get another one. They have learned not to ask again.
We also bring a backpack full of snacks into the parks. That way no one gets hangry! I try to buy new to them snacks or something that is special, so they are more inclined to eat. They just want to go, go, go all the time in the parks.
We also usually bring muffins with us for breakfast. Saves $$ and time when we are there at rope drop. We eat on our walk into the parks.
OP, I don't know where you are staying, but if it has a microwave, we have saved money on dinners by bringing soup, individual cups of of mac n cheese, and once I made a huge batch of spaghetti at home and froze it. We ate about 3 meals from that. LOL. We live in NorCal and drove to the parks. So we had a cooler and then kept it in the fridge in our room. I realize if you are flying that would not work. Just throwing out more ideas.
We also bring in glow sticks from the dollar store because my kids always want all the light up stuff they sell. Much cheaper alternative!
If you do eat in the parks, a lot of places have portions large enough to share as well.
Have a great time!