This sounds like a much needed service on the island. I feel sorry for parents that have to lug all that stuff along with them. Rent it there, leave it there. Great idea! Hey, that would be a good advertisement: Rent It Here - Leave It Here.
I hope you don't mind me piggy backing on your post, but this is a suggestion for visitors with kids. When we were visiting on AC we found that the easiest and cheapest way to keep lots of water on hand is to purchase it at the water distributor. The one we used is south of town, a couple blocks inland before Banyon Bay. A local will give directions. Buy four gallon jugs to start out with. They are square, with a handle and fit nicely in the refrigerator. Also buy a 5 gallon jug to refill the smaller ones. You will need to hitch a ride if you don't have a golf cart.
Belize has the powdered drink mix, Tang. It comes in lots of flavors. Orange, Tangerine, Pineapple, Strawberry and it is so much better than our stuff in the States. We would buy the big packets and mix it up in the 1 gallon water jugs. We would always have 2 flavors ice cold and ready for the thirsty kids. It has vitamin C and calcium. Much better and cheaper than sodas.
Have fun! You and the kiddies will never forget this trip.