Hi, Angie! For traveling on a budget, you might want to consider staying at a
Value Resort on the Disney property. There are 4 to choose from each with a distinctive theme. Regardless of which you choose, you will get swimming pools, a food court, and best of all, the use of Disney's Magical Express. This service will drive you to and from Orlando International Airport, and even deliver your bags right to your room. No need to rent a car, find a taxi, or get your luggage. You will find this to be very helpful, especially with 2 small children.
The rooms at the Value Resorts are not huge, but they are clean and comfortable. For an additional fee, you can even rent a refrigerator to keep milk and snacks right in your room.
For more information on staying at a Disney Resort on a budget, click
HERE. I hope you find a resort that fits your budget and your family's needs! Have fun!