Hello fellow Kentuckian!
We might just see you there next fall, because October is our favorite month to visit Disney and we do so every year! If you haven't tried it before, consider attending Mickey's Not So Scary Halloween Party. It's so much fun, and tops my family's Disney must-do list year after year.
In your position I think the most important factor will be the size of your family. With 3 children, the moderate resorts that could accommodate your family are Port Orleans-Riverside (in the Alligator Bayou section) and the cabins at Ft. Wilderness. At Port Orleans you will find two double beds and one pull-out trundle bed. At Ft. Wilderness you could rent a cabin that sleeps 6, with a double bed and bunk beds in the bedroom, and a fold-down Murphy bed in the living room. There you would also have a full-sized kitchen, which is great if you'd like to prepare any of your own meals or just have a nice midnight snack. And no need to worry about dishes on vacation - Mousekeeping will even load the dishwasher for you!
Another option would be to consider the family suites at the All-Star Music resort. These rooms also sleep up to six guests, with a separate bedroom, kitchenette, and the added bonus of having two bathrooms - a real plus with teens/tweens in the family!
You can see a complete list of resort options for larger families
here.
Have a great vacation!