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.