If you want to stay on Disney Property then check out our Disney Resorts Board. If you prefer to stay off site then we have an Orland Hotels board that you can look at and ask questions there. You have a lot of options so good luck in your search!
Check out the Villas at Wilderness Lodge. They sleep larger numbers. As far as I know, once you are on property, you can use the ammenities of that property.
Four kids? What are the ages of travelers? How many days are you thinking. Renting is a great idea. You'll get deluxe accom. and everything that goes with staying on site (emh, me, buses, etc).