Check the DISboards for one of the fridge swaps...they're free, just takes a little bit of time and effort to get them (ok, maybe not totally free since it's generally something you tip the CM who delivers it, but if you haul it back down to the luggage room yourself, no tip for return). MUCH cheaper than renting from Disney.
It sounds like you're wanting drinks and snacks for inside your room, so consider getting the refillable mugs. I think they're about $12 each but then you can get all the soda/milk/juice/tea that you want from the resort food court. It looks like you have two kids so around $24 and you've got all the drink they can handle.
For inside the parks, we just got free water. ALL of the counter service places will give you a free cup of ice cold water for the asking. If your kids aren't plain water drinkers, then brink along some of the flavor packets (Crystal Light is the name brand, but
Walmart has a generic brand that is just as tasty but half the cost). Half a pack in a small cup of water (so with two kids, get two waters and split the flavoring)....a straw to stir and thirst gone!
Others have given you great advice about sharing CS meals....we are one adult and two teens and we typically get 2 CS meals and it's more than enough for all three of us. We rarely get snacks in Disney, too busy, not hungry. Bring a few things for the room, but honestly we always came back to the room so tired that food was rarely on our mind.
Since you're only talking 5 days, one or two boxes of cereal should suffice for breakfast and not take up a huge amount of space. Milk can be brought back to the room in a refillable mug, then if needed you can still go back to the food court and get something to drink in the mug, there is no limit to how many times you can refill. The room created in your suitcase for the two boxes of cereal can then be used for souveniors (even if you don't buy souveniors, there are always mementos to bring home...the "I'm Celebrating" or "Honorary Citizen of Disney" pins are musts for us.....many many maps so that the kids can play with them at home and relive their journey, ok, we're weird enough that we also bring home handfuls of the Disney napkins to use at home (after one goes in each scrapbook). etc.