In order to budget out how much you might spend on food, go through and do a sample "dining tour" for each day. Figure out where you might eat, what you might order, what tax and tip will be, what snacks you might want, etc. Add it all up and you'll have an idea of what you might actually spend.
A lot of it depends on if you have any big eaters. I suspect the 14 yr-old can pack it away.

However, I doubt your 7 yr-old eats much. When my family of 4 went last year (DH, me, DS10, DD7), we spent less on food than what it would have cost us to get the DP. Now, part of that was due to our "adult" 10-year-old eating kids meals. However, DH and I usually split counter service meals, then bought each kid their own kids meal.
Also, to really add up the cost of the dining plan, you have to figure out not only the cost of the DP itself, but also the difference it would cost you to pay rack rate for the room. I got our room with a
AAA discount and got our tickets on a special through
Undercover Tourist. By the time you added up what the dining plan would cost us *as well as* figure in rack rate for the room at tickets, we could eat for way less.
Hmmm, going back and figuring things up -- we ended up spending, per day, about what the dining plan would have cost us. However, it wasn't worth losing our discounts on the room and the tickets to get the DP. I hope that makes sense.