No offense to you, but I get really tired of hearing people complain, be worried, etc... about going to WDW knowing it will be hot and humid when they go. Goodness sakes, guys, you know what the weather will be like when you go. Either quit complaining about the weather when you are planning to go, or plan a different (cooler) time to go!! What is hard about that? It's not like anyone is making you go to WDW, you are choosing to go. And why not - it is after all the happiest place on Earth!
We went last July the week after the 4th, and are going this July the week after the 4th again. It was extremely hot and humid last year for the 8 days we went, and we expect it to be the same this year, too. But you know what? You're at WDW!! How bad can it be, really? There are plenty of indoor shows/rides, etc... that you can cool off in. We have 2 kids, who last year were DS 7 and DD 4, and they made it ALL DAY at the parks, no nap or anything. We rented a double stroller everyday we were at a park, and they simply got in it if they wanted to and walked if they wanted to. They felt a lot better KNOWING that if they wanted to, there was a stroller there for them. The DD stayed in it quite a bit, and the DS off and on during the day, but that's all they needed. We got them each a misting fan before we went ($5 at Wal-Mart or $17 at Disney, you decide where to purchase), and they kept that running non-stop all day, but that was a lifesaver. We did not go back to the resort at lunch for a swim, nap, etc..., b/c we didn't want to. And our kids did fine. We have traveled with them a lot since they were born, so they're used to having their schedules rearranged and "out of whack" on vacation. However, your kids may be different. But I never wanted my kids' "schedules" to rule how our vacations were, and they don't to this day. If you keep the kids relatively cool and happy, and don't make them walk everywhere but give them the option to ride if they would like, they should be fine.
Just my 2 cent's worth!