OMG WHY?!?!? You are crazy!!!!!
That said, The WDW monorail transportation system is pretty good so it's possible to get around all four theme parks, assuming you start out early and run around all day.
Saturdays are actually not that bad at WDW because the majority of visitors are not local, and they use the weekend to travel. That's a complete flip of Anaheim, where they've had to come up with all sorts of contorted methods to reduce local (annual passholder) crowds who inundate the parks on the weekends (especially Saturday).
So if you're visiting Disneyland in California, either avoid the weekends, or check the annual passholder blockout dates and go during the times when the locals are shut out (peak summer days, holiday seasons, etc.).
Two more very important tips, since sheep_jeep was able to hop on attractions with no more than a 5-minute wait... sheep_jeep, when did you go on this trip? It's possible to do standby walk-ons onto a lot of attractions during the slow season (and I tend to not plan in advance so I do the same thing), but if there are any rides you REALLY want to go on, you ABSOLUTELY must get a Fastpass in advance. They're essentially a placeholder you get in advance that reserves a window of time for you to go on a ride.
Some rides are extremely popular. *IF* you are picky about what rides you want to do, you're going to be pretty frustrated that all you can mange is five rides in a day (when you are paying $120 to go into the park and mostly just stand in line).
Good example: Disney's Animal Kingdom opened their new Avatar-themed land last year (remember that old James Cameron SF/Fantasy movie with the tall blue people?). They have a ride there called "Avatar Flight of Passage" that SINGLEHANDEDLY put the Disney Parks and Resorts division in the black last year (OK maybe that's a bit of an exaggeration... but not by much).
I just looked up the standby wait time right this very second. 230 MINUTES. If you went to Animal Kingdom right now and went to stand in line, you will be in line for almost four hours to get on this ride. And it's almost impossible to get a Fastpass if you don't grab one the moment you're able.
...which brings me to my last point.
If your kids have their heart set on meeting certain characters, at least in WDW in Florida, they've got it down to a science where you can get Fastpass reservations for meet-and-greets. But you have to plan it in advance. The moment you know you're going, buy your park tickets in advance so you're able to use the My Disney Experience smartphone app to pick up Fastpasses for everyone. You're limited to how many you can get in advance, but if you get the ones that are really important, it's one huge stresser off your back.