How about Holiday Inn Family Suites? If you get connecting suites, you can get everything you have asked for.
It is close to WDW - less than 5 minutes from EPCOT and less than 10 minutes from MK. It is also very convenient (about 10 minutes) to Seaworld and Universal since it is just off Interstate 4). The hotel is only a few years old so everything is bright and modern. It is still a Holiday Inn however, not the Ritz Carlton. We think it is at least as nice as the Disney Moderate Resorts.
Most suites have 2 bedrooms. If you wanted the whirlpool however, you would have to get connecting suites. The whirlpool suite (called a "sweetheart suite") has only 1 bedroom. You could probably get 2 connecting suites for about the price of 1 Wilderness Villa and there would be 3 bedrooms altogether.
Fridge - yes they have them, as well as a microwave, in each suite
Room Service was available from around 7am until about 10pm the last time I was there.
There are 2 pools, a large plain olympic style pool as well as a family pool. The family pool is zero entry and has a waterfall and water toys built into the pool for the kids to play with. You can also rent pool floats and toys for the kids. There are plenty of chairs as well as a pool bar and snack shack.
There is a sit down restaurant that has a buffet or you can order off a menu. Not the best food in the world but adequate. There is also a convenience store and a fast food restaurant with A&W (burgers, chicken) and Pizza Hut items. There is also a pretty good hot breakfast buffet that is free for everyone in the room. This might help since you don't like to get in the car for every meal, and helps if you want to get an early start in the morning.
As I mentioned above, there is one suite type with a whirlpool tub, but it only has one bedroom. They have a workout room, but I haven't used it so I can't really tell you how good it is.
For the kids, in addition to the pool, there is a game room. They also have nightly activities like bingo and face painting. There is Nintendo in the room and you can rent Nintendo games or videos for the TV. Each suite has a TV in each bedroom and in the livingroom. If you got the sweetheart suite and the connecting suite you would have 3 bedrooms and 5 TV's. I don't know how many kids you have but that might help to minimize the arguments over the TV.
My kids (9 and 6) love the place. Check out their website at
www.hifamilysuites.com. Good luck with your search.