Hi, Dave!
Walt Disney World Parks and Resort cater to parties of all size. We will be able to find you the perfect accommodations for your group. You might want to start on the official Disney Web site, which offers a
good overview of the options available to larger parties.
Truth be told, most of the rooms built for larger parties do come equipped with kitchen areas or kitchenettes. If this is a deal-breaker, you will probably want to consider two rooms. Many of the Resorts do offer connecting rooms; depending upon availability the Cast member who assists you at check-in will do his/her best to honor your request.
Without knowing your budgetary guidelines, my instinct is to recommend
The Cabins at Fort Wilderness, a Resort in the Moderate class. Each Cabin does sleep up to six: Guests and is equipped with a full kitchen, should you choose to use it for snacks and drinks.
Based on the ages of the children in your party, I'd think they would get a great deal of use out of the green spaces that abound in the area, including nature trails and playgrounds. There's a fantastic pool, recently renovated, and lots of room to run and play.
Another draw is the nightly movie: Chip and Dale host their Guests at a campfire (with s'mores ingredients available for purchase - or bring your own!) featuring comedy, music, and a family-friendly Disney film. Chip & Dale's Campfire Sing-A-Long is held every evening, weather permitting.
Have a wonderful stay, wherever you choose!
See you later, celebrator,
-Deborah B.