If you do arrive at noon, odds are you can do Indy. (The ride does "go down" fairly often--in June 2009 we passed it probably at least 3 times when it wasn't running; it usually goes back up pretty quickly though. But if it's "down" when you walk by, it will not be giving out FPs until it's up again.)
The quickest way for just ONE adult to get Indy (and perhaps also Splash?) is the single rider line, but that would leave your 6-year-old out in the cold. Or the hot as the case may be.
If you're in the area, Big Thunder Mountain Railroad FPs are usually available later in the day, if that interests you (child swap). You could most likely get one at 2 PM for with an OK return time.
On a super-busy day, Monsters Inc. could easily have a 10-15 minute wait (I think that's what we had in June 2009). It's not a bad wait--I kind of wish the wait WAS consistently 10 or maybe 15 minutes, because the interior portion of the queue is really interesting. As long as it exists, I imagine Muppetvision will always be a cool and not-crowded place to escape the sun. I think they might have coloring sheets for the little ones as you wait for the show. (No chairs but many people sit on the carpet.) If your kids like Playhouse Disney, they have a show too, also in DCA. There's the small "Drawn to the Magic" show nearby as well; it's pretty cute and if your kids need to meet Mickey that first day, they can probably meet him at the end if you hurry over to him.
The main issue is that DCA as a whole might be crazy-busy due to World of Color, but even if that's the case, I think the rides and attractions that will "feel" it the most will be the thrill rides and the ones that strongly appeal to adults, more than the 3-D movies (which have little repeat value for locals) and the shows that kids enjoy more than their parents. Due to World of Color attracting everyone to DCA, though, I'd probably save the Pixar Play Parade and Aladdin for another day, and if DCA is just unbearably crowded, ignore my advice outright and stay in DL, which is at least used to crowds.
Worst case, go to Downtown Disney for a break.
Disneyland's parade-ish thing (if running) will probably be less busy than the Pixar Play Parade, though I agree if you do want a great seat, an hour wait isn't a bad idea. Many AP-holders don't love that parade but the parks are going to be packed and I'm sure a lot of people in attendance would like to see it! (IF your family can do a late lunch, you could sit down, send a runner for food, and then eat it as you wait.)
Basically, I'd say just go with the flow as much as possible and try not to stres--it'll be a super-busy day, but the days that follow should be lighter.
Have a great trip!
