Another vote for the cabins, here. I just reserved 3 of them for our trip in February. Our group (3 families--us(6), SIL(4), and MIL(2)) opted for the Ft. Wilderness over the Polynesian concierge!
We (just my family) stayed there a couple years ago, and wanted to try a different resort, but something just kept steering us back to FW!
We consider the kitchens to be a huge plus. Even if you don't plan on having a formal "meal" there, it is so handy to have that fridge for your bottled water, snacks, milk for cereal, cream cheese for bagels, lunch meat, etc. (Beer & wine??
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We also enjoyed having the extra bedroom. We were able to put the kids to bed, shut the door, and enjoy some quiet time to ourselves without worrying about waking the kids up.
Most kids are just happy to have a pool to swim in and don't really need all of the bells & whistles. They will certainly enjoy the petting farm & other activities around FW. I want to go fishing this year, and catch the evening campfire and movie!
My SIL has two boys aged 13 and 7 and I know they will like having a little more room to spread out and run around the cabin loop. It is definitely more relaxed than other resorts, and I think that is a huge plus, after all of the hustle and bustle of the parks.
If you can afford it, I would recommend renting a golf cart, and reserving it as soon as possible. We had no idea they were available when we showed up last time, and silly us called the Bike Barn to see if there was one to rent. Ha ha! Apparently they sell out quick! I just reserved 3 of them today for our trip. ($45.58 a day incl. tax held with a credit card #)
Good luck on your decision, and print out this thread and let your family read it--hopefully that will convince them!
Wendy