It sounds like you have a great vacation planned. You mentioned $2,000 for food, so I tried to break it down to see if it made sense. That is roughly 9 days at about $200/day.
(9 x $200 = $1,800 w/ $200 left over to buy breakfast items.)
With your $200/day, you could allocate about $80/lunch and $80/dinner and $40/snacks during the day. That seems like more than enough to me. Actually, depending on your family's spending habits, that could easily include souvenirs, etc. (Dinner at Friday's or Chili's for two adults and two kids doesn't cost more than $40...does it? I'm not sure. It's been a while since we've eaten at a Friday's or Chili's, but especially with kid's meals prices that seems very doable.)
I'm guessing water bottles at Disney run around $5 (hopefully less) and allocated $5 per person for a snack and a water bottle bought at Disney. (That would be about $40/day.)
Here's an idea...when we travel with our children, we often eat breakfast in the hotel. (Either purchased by me or we book a hotel with breakfast included.) Then, I take cereal bars, fruit, etc. with me for a snack. (That helps hold everyone over through the normal "busy" lunch time.) We leave the touristy area in the afternoon...when it is the hottest and everyone needs a break. We usually look for a sit down restaurant...Applebees, Chili's , etc. and eat a late lunch...around 2 or so. (The resaurant isn't busy and everyone enjoys a quiet restful meal.) Then, we go back to the park late afternoon/early evening and take a break for a smaller meal later. We've tried to make it a habit to not eat more than one meal/day at a place like Disney. It seems to do everyone in our family good to get off the grounds and the prices are much lower, too.
I don't know if this helps....but I think you could easily satisfy your food budget with $2,000 and depending on your choices have money left over!
Have a great time in Disney!!