Hi, Melanie!
Several of the resorts do have king size beds. However, when you get this option, there is just the one bed in the room. If you have kids, you may want to book 2 rooms and ask for connecting rooms so your room will have the king size bed and the connecting room can accommodate the kids with 2 beds. When booking you will need to book a KING room as these are limited.
One option that might work for you is at the
Grand Floridian. Some rooms have a king bed with a full size sleeper sofa. If your kids do not mind a pull-out bed, this might work for you!
To simplify, get your dates nailed down and call a friendly Disney Reservationist at (407)W-DISNEY. Explain your situation and see what options are offered. It can be done, you will just have to get a bit creative about it!
Sending pixie dust and happy wishes that you find the perfect resort room to suit your family's needs.