With the heat and humidity here, I would be very selective on which items I would be bringing into the park for lunch. Trying to keep things cold/cool is a battle.
I would go the big breakfast route, bagels/ cream cheese, salmon, cereals, milk, juice, some type of protein, messy omelets or scrambles whatever you prefer to call them, fruit like strawberries, kiwi...
I would carry with you a couple of apples, oranges, tangerines, something that can with stand being in the backpack. Some type of granola bar or protein bar again watch which ones as everything sorta melts, dried fruit raisin, cherries or a mix, I hit up Aldi and make my own trail mix, individual/single serve crackers chips, pop corn ..... Bottles of water you can refill they will give you water and ice at the QS locations.
You can share QS meals super easy, for our family of four when the girls were teenagers, we could share 2 meals and get and order of chicken fingers, or and extra side.
You could also do a TS meal and share... We would head into Rainforest at AK, share the Awesome appetizer Adventure for 19.99 and a order of onion rings for 4.99 and soft drinks and be out the door at around 50.00 bucks... If we were really hungry we would get the Awesome Appetizer 19.99 and the Beef Lava Nachos 17.99 with soft drinks and be out the door for around 70.00. We would grab dessert Mickey ears in the park later on.
Then I would stick to making a deli bar for when you get back to your resort, bread, deli meat and cheese, deli potato salad, macaroni salad, cole slaw, guacamole and hummus with chips, carrot / celery sticks with ranch or blue cheese dip. If you have a oven you can get some frozen fries, cheese sticks, or see what other oven made options you can come up with.
Our friends stay off site at Orange lakes or West Gate, and on arrival day, they stop at Publix load up on groceries for the week, and place a to go order at Olive Garden swing by and pick it up on the way to the resort, they order a pan of lasagna, and a pan chicken parm. with a extra containers of sauce and a pan shrimp alfredo which is what the eat for dinner the 1st night.. It comes with salad and bread sticks... They munch off of that for 2 or 3 days. They live on a farm and ranch and the nearest Olive Garden is about 300 miles, so this is a really treat for them...
I would take time to look at the menus and do some homework on what would work for you family, being prepared is your most important tool to saving money.