Stacy, don't be stressed, it's supposed to be a vacation. Destress and keep repeating it to yourself. I am going the week after you and feel more stressed about trying to get things done with my vehicle and home before I go than about vacation. Stop worrying. You have enough money for food, snacks and sourvenirs.
If you feel that you have to budget this is what I would do. Stop on way to resort and pickup snacks/water and soft drinks to keep in room (believe it or not this does keep the snack budget down - especially if you bring a water and bag of chips in the parks with you) and maybe some cereal/cer. bars, muffins, milk/juice for breakfast (these items shouldn't cost over $35 if bought offsite).
Most people eat at counter service rest but if you want a good sit down meal, set a ps for lunch everyday or every other day. That way you are limiting your counter service meals to once a day or twice every other day which leaves a little variety inbetween. Next, you and daughter may want to consider splitting some of the counter meals. Last year I ate at Columbia Harbor House (MK) and Electric Umbrella (Epcot) a couple of times. All of those times, I could've easily split my meal (I went solo last year so no one to split them with) and I know that I can eat some food. This year mom and I are going and I intend to split a meal or two with her (at Col. HH there is a fish/chicken strip combo type meal, mom gets the two fish stips, I get the two chicken strips and we split the fries which there are a ton of, order a second drink but save 2nd meal cost and there is no waste/food left over to throw away). I also eat snacks or cereal when back in the room at night.
I always have ziplock bags in backpack for the parks. I find the zip locks wonderful as I keep things dry from the water rides (all film, movie camers, etc get put in them) but not to mention that whatever food is left over for meals gets put in them as well and you can choose to snack on them or leave them to be snacked on at night.
I say by morning of day 4, take a look at the $$ you have left and plan accordingly (maybe set another ps or two, or begin to really splurge here and there). At that point leave souvenir money on the side. A great thing for souvenirs is to look around all week, make a list of those things that you may want to purchase, the $$ of the item and where the item can be found. On your last day or two, have the kids and yourself review the list and make a decision on what they really want then go purchase it. That way there are no true impulse purchases and everyone gets something that they want
I have a food budget for 2 people for 9 days of about $900. 7 days on property. I have a sitdown meal planned for 6 of the 7 days (2 dinners at Le Cellier, generally $80 each dinner) and 4 dinner buffets. I have purchased a few Q&C vouchers and I have a disney rewards card with enough $$ to cover the rest of counter lunches. I will probably spend about $125-200 on souvenirs (depends on how many pins I want to purchase). I know that I'll buy at least one bag of popcorn everyother day and one icecream everyday as well. We eat breakfast in our rooms while getting ready and we bring fannypacks and a backpack (usually store backpack in locker, has rain gear, water and snacks) and we walk back to get the occasional snack out it maybe twice a day). I find this works out well for me and does keep cost down and I never feel hungry at all.
Don't worry, you've got enough money and no one will starve. Have a great vacation with your kids.