Wilderness Lodge.
It's a beautiful hotel that is very relaxing for kids. They have a playground, beach, good pool for little kids (small slide), kiddie pool, etc. There is a pathway to Ft. Wilderness where there is a petting farm, campfire sing a longs, etc. You can rent surrey bikes at the dock and ride the trail as a family. You can rent little boats to take on the lake. There is a nice boat to Magic Kingdom, which is fun for kids.
The AKL's only advantage over the WL is the zero entry pool. However, I would not personally choose it for such young kids, as you have to rely on the buses to get everywhere and it's pretty far removed from the Magic Kingdom, especially.
If you want to stay at a Moderate, I'd look at the Port Orleans. However, be aware that the beds at the moderates are FULL size, not Queens. They can be a tight squeeze for couples used to a Queen or King bed at home. Plus, the rooms are smaller, so fitting a pack and play in there will make it a tight squeeze.
Look into the Swan/Dolphin to see if you are eligible for any of their special rates. The rooms are nice, there is a great playground onsite and the pool is really good also. Not a Disney resort, but considered one of the Epcot resorts, and you can walk to Epcot and the Studios.