My best advice here is SKIP THE KIDS MEALS. They are a horrible value for the amount of food you get. If your kids are young, share an adult CS meal with them. A slice of pizza from Alien Pizza Planet or Boardwalk Pizza is HUGE and about $8. Definitely enough for 2 kids to share one slice and just supplement with a fruit or veggie side or some Gogo squeeze or something. Also, you can buy a lot of CS stuff "a la carte" for less money than the combo meal. At Plaza Inn, for example, you can buy single pieces of chicken, sides of mashed potatoes or veggies, biscuits, etc, so you can piecemeal or supplement a full platter so you have enough to share. You can order the fries as a side most places, can order the burger without the fries, etc. Hit up the produce stands for some fruits or veggies that everyone likes and split them between meals.
Don't bother leaving property. You won't save much and will waste a lot of time. Just share stuff. Portions are huge.
Also, it goes without saying, but if you are on a budget DO NOT buy soda. Period. It's ridiculous what they charge in the parks for a soda. Bring refillable water bottles and just drink water.