Weather can be anywhere from comfortable to cold. Friends of mine have pictures from one Thanksgiving trip and they're all wearing winter coats, hats and gloves! But I've also gone the week after Thanksgiving and enjoyed temps in the high 80's. There's no predicting what it will be,
As others have pointed out, you're not going to get 4 connecting rooms. I would recommend 2 Family Suites at AoA or ASMu. You can request that they are adjoining (close to each other) and you can use one of those rooms as a central meeting place. The advantage would be having a kitchenette in each of the suites so that you can prepare a quick breakfast before heading out to the parks or light lunches for those days that you choose to spend at the pool.
A Grand Villa (a 3-BR DVC villa) would be very expensive but would accommodate your entire family in one space. A couple of people would be sleeping on a sofa bed but you would have 3-4 bathrooms and a full size washer/dryer right in your villa as well as a kitchen, full dining room table and enough seating for everyone to eat at the same time. But the price, even with renting points, is very high. If I didn't own DVC, my upcoming week-long stay in a BWV GV would cost me over $9K to rent thru an agency.
A more economical option would be to rent a vacation home off property. Many of them are extremely nice, with game rooms, home entertainment theaters, private pools and outdoor kitchens for barbecuing. And they can be quite affordable. You might want to check HomeAway or VRBO if you want to get an idea of what your money can get you when you're offsite.