Hi Kenyon,
Of those 3 options, I would choose the
Polynesian Resort hands down. Location is a very important factor if you are using Disney transportation with little children. You'll be very close to the Magic Kingdom this way, which is where you'll likely spend a lot of your time with toddlers.
Honestly, while the kitchen is a nice perk, are you going to want to cook while on vacation? Your room at the Poly will have a mini refrigerator which is great.
Old Key West Villa's are beautiful and do have extra space, however they are a considerable distance from all of the theme parks. The Cabins at Fort Wilderness also have extra space, but without a rental car, the transportation can be very time consuming from them.
Hope this helps and have a wonderful vacation,
Kaylene