I think staying near the Magic Kingdom is great for convienience. When I was a kid, we stayed at Ft. Wilderness. Twice we brought our RV, but once we stayed at the Cabins. They are reasonably priced for the space and full kitchen you get.
Plus, get you and your little ones up and around early, hit the parks before it gets too hot or crowded, eat a character lunch in the park, then when they're pooped, head back to FW and take a nap, swim in one of the pools, or do one of the MILLION things there are to do at FW. Then eat a quick dinner you cook yourself in your cabin, and head back for another go around. It's easy to get to MK (by motor launch...which kids LOVE!) or Epcot (take bus to TTC, or take the motor launch to contemporary, monorail to TTC, then the other monorail to Epcot) There are also buses that run to AK and MGM (of course).
This allows you to make the most of the parks without wearing the kids out (or you!), and you take advantage of all the other cool things to do in WDW...also the kids will LOVE the nightly Campfire/Movie at FW! And you will love that you only have to walk back to your camp site once it's over to put the kids in bed!
Also, I agree that May is the time to go. We went once to WDW AS SOON as school let out and beat much of the summer rush. It was warm, but not ridiculously crowded.
Best of Luck!