Need at least 3 sleeping surfaces.
So I'm not nearly an expert on moderate resorts, but if I'm not mistaken, they all don't have that extra bed/daybed/sofabed. We also have 2 kids but need the 3rd bed as our kids are older, so I've done a bit of research on this in the past. We stayed at POR last year thinking that the pull-down bed would be fine for our 12 year old. It was indeed "ok," but she had to stay curled up on her side and couldn't move around much. I'm not sure how the other moderates are as far as a daybed.
In your shoes, I'd price out the lowest cost deluxe resorts -- Contemporary garden wing room first. It's a large room and has a daybed. And you will have a walking path to MK.
Wilderness Lodge will give you boat access to MK, but you'd need to request a bunk bed room (I'm not sure if it's a bookable category?). Same with Animal Kingdom Lodge -- you'd need a bunk bed room and I'm not sure if it's a booking category or just a request.
You could price out standard rooms at Boardwalk or Beach Club. But I *think* a daybed is just a request at those resorts. They both offer walking paths to both Epcot and HS.
Polynesian and Grand Floridian give you a daybed, but they are pretty high priced resorts. Of course, they just happen to be our favorites! They have monorail access to MK and Epcot.
Fort Wilderness has always intrigued us, but the spread-out property has held us back. I believe the cabins would accomodate your sleeping arrangements, though.
