Yes, stay in the parks if it rains.
Last year, our first morning pulling into MK parking lot, the dark clouds were as far as the eye could see. My DS8 HATES storms, but loves learning about weather. Since this was his birthday trip the decision was his, go for it or not. He wanted to go. Threw on the dollar store ponchos and headed for the tram. By the time we got in the park, it had stopped raining and no one was there, at least for an hour or so. Got on many rides right away.
Watched many potential thunderstorm clouds move in, with no rain (a bit of thunder was all you would hear), throughout the day. Park was almost empty. I guess folks thought it would rain and didn't bother trying to come in or staying.
The year before that though, our last night, we missed fireworks due to a MASSIVE Florida thunderstorm that moved in, that "puppy" wasn't going anywhere. We camped that year, off site and ended up getting a motel room near by. The tent was a mess and soaked. It was still storming when we got to the campsite, and the youngest DS wouldn't stay. I still have a hard time getting him to camp anywhere because of that one night (YES, it was that bad). They move in and move out quickly in Florida, so your chances are good it will be short lived.
On a side note, after our Sept. trip we are planning a few weekend trips and he said he wanted to camp on of those times, so he may be snapping out of it.