For first-times, I always suggest going to MK first, especially for kids. The early morning for monday and Tuesday are about the same. Yes it will be crowded, but it's only two days and you'll get over it.
Your 6 YO may not meet the height restrictions for Space Mountain (44") and Splash and Thunder (both 40").
That being said, get there 1/2 hour before opening. By "there" I mean at the entrance to the park (not to the parking lot). If you're staying off-site, allow another 30-60 minutes.
Go to Space Mountain, Buzz (there close to each other), then run across the park to Splash Mountain. If the wait is less than 20 mins, get in line. Otherwise, grab a Fast Pass and go to Thunder Mountain.
Next you need to go back towards the back o fthe castle to see Mickey's PhilarMagic and perhaps Peter Pan (use FP for this if necessary).
This is a lot of running and moving in the early morning, but you've just completed seeing the most popular rides (which will have extremely long lines later in the day).
If you aren't making Priority Seating arrangements, you can easily grab a counter-service lunch at noe the tomorrowland restaurants. But I suggest leaving around 12-1 and getting on the monorail to the Contemporary resort (it's very simple to do). You can usually get a table at the Concourse Steakhouse with little wait. This a very casual, quiet place to eat and relax.
when you go back to the park (again by monorail), it will be very crowded. However, there are many attrations that you can either walk on to with no wait, or where the wait line is in A/C so it's not too tough: Transit Authority; Tiki Birds, Hall of Presidents, Pirates, Time Keeper. - and the Train that goes around WDW. The lines for Haunted Mansion and Country Bears seem to come and go - either get a FP or be perpaed to wait for 30-60 minutes.
As far as the 2nd park, you'll find that all three have their fans on this discussion board. My 8 and 12YO boys like MGM beucase of RnRC and ToT. It also has their favorite eatery - Scii-Fi Dine In. But my biggest reason to urge you to go to MGM is that it has (by most opinions) the best noghttime show of all WDW (and probably Florida) - in Fantasmic!. It would be a great way to cap off your first trip to WDW.
Note, if you do go to MGM or EPCOT, I strongly suggest you make Priority Seatng arrangements for both lunch and dinner. There's no cost and you'll be glad you did.