We travel with either 3 or 4 children, regularly. We found this last time that splitting meals between DH and I and buying a side salad for us gave us a good amount of food and filled us up without leftovers or feeling overstuffed. I picked up the fried chicken dinner at Plaza Inn while we were waiting for the fireworks and it was a 1/2 chicken with mashed potatoes and vegies and a biscuit and ordered a salad and it was just perfect for us. I had a bunch of people ask me where I got my food - since I was sitting at the top of the hub eating on a real plate with real silverware. I think people were surprised!
We always take snacks and that helps with buying snacky things that can get expensive. We usually have one splurge sort of snack when we are there - a mickey rice krispie or ice cream or whatever, but not every day. We don't do it at home, so we don't feel the need to do it there. I usually buy snacks that they don't always get at home. And beef jerky is a big hit for a snack for my kids. We try to mix up food choices when we are there since my kids would just as soon choose chicken nuggets or cheeseburgers for every meal. But it can get hard.
We have ordered pizza from Papa John's for delivery to our hotel before and that was good, but it was way too much and the hotel didn't have a micro, so it was cold pizza (yuck!) if you wanted any leftovers.
We did go to Mimi's for dinner and they have such big portions that DH and I split again and they don't charge a split plate fee. Our server did give us a little more salad than he might have normally, but everything else was just split in half.
You could also consider a fruit plate or at Whitewater Snacks they have a smaller fruit portion that makes a great snack for later and helps everyone stay hydrated and it's a little healthier.
My DSis went a little before we did in May and they only did one purchased meal per day. They had breakfast at their hotel - they had a fridge and micro in their room and had cereal or the micro breakfast sandwiches or bagels or whatever. They made sandwiches and brought chips/crackers, juice boxes and some other snacky things with them into the parks and did just fine. My sis had a soft-sided cooler that is a little bigger than a lunch box that she used and had frozen water bottles to keep her food cold.
We also eat breakfast in our hotel room since we stay at HoJo and have a fridge and micro in our room. That can save a bundle. My kids eat cereal at home for breakfast most of the time anyway.

DH and our DS 13 like the breakfast sandwiches.
You might have a harder time with your teen ish kids and sharing since teenagers, in my experience, seem to always be hungry! One fun thing that we always get when we go to DLR is the Kettle Corn in DTD. There is a stand right near the tram stop and we always get the biggest bag. It's a huge hit for our fam.