Which restaurants have really big portions? And will they give extra plates for my under 3 boys?
Pretty much everywhere.
Including many Counter Service locations. The half-chicken-and-ribs-with-potatoes-and-green beans plate at Cosmic Ray's in MK, for example, is about $14 and could easily feed 2 adults with no problem, so sharing with little ones would not make a dent.
Extra plates are never a problem.
Just be aware that, naturally, less cost-intensive dishes will be presented in larger portions. Chicken, pasta, tilapia/mahi mahi, pot roast, casseroles, burgers will be huge portions; steaks, scallops, chops, sea bass/salmon/ahi tuna, crab, lobster - these type of entrees will be in smaller (relatively) portions.
When traveling two years ago with a then-18-month-old, we often ordered him his own dish of mac and cheese or mashed potatoes when we were at a table service restaurant; we were only charged for it a couple of times out of five dinners, and when we were it was only $3-4. Something you might want to think about if you need to slightly supplement the food y'all are sharing. We were never charged for his beverages, even when we ordered milk.