All of the stuff you are saying is what makes it so hard to figure out what to do! I really don't know how my kids would be. I would plan to get to the parks by rope drop, do as much as we can until lunchtime, then come back to the resort to relax or swim. Possibly go back out later that evening, but possibly not. I don't see my girls taking a nap by then, my oldest doesn't nap now. But they are a bit prissy now. it's hard for me to imagine my girls tolerating all of that heat for so long, lol. It will be our first trip, so a lot I just have the guess.
I would stay onsite if it is your 1st trip. No logical reason except I'm glad I stayed onsite my 1st trip.

We'll be staying in a 2 bedroom condo and renting a car to drive to and from the parks. They have a very nice pool/water slide/playground area for the kids and since we usually plan at least one non park day to do whatever, this'll be a really great option for us. I'll bring a few Disney party decorations to decorate the kids bedroom so it feels a bit more Disney to them, but I think it will be a great stay.
But since I don't anticipate this being our only Disney trip, maybe offsite would make a bit more sense when my girls are older and we really might need the space, and once I was a little more familiar with how to get around the area. 
