This is somewhat of a repeat of what others said, but my thoughts are:
1 - As far as parks, AK is a great choice, and I'd spend any and all remaining time in the MK, which offers the most attractions (placed much more closely together, meaning fewer steps for little legs) for young children. I wouldn't bother with the water parks (or with the hefty ticket upcharge), as they don't have a whole lot for youngsters. If you have an extra half-day, the kids might enjoy a number of attractions in Future World, Epcot (e.g., Seas with Nemo, Turtle Talk with Crush, Character Spot, etc.) or in Hollywood Studios (Disney, Jr. show, Toy Story Midway Mania), depending on their particular areas of interest. Also, you asked about how to tour MK: my advice is to choose one or two adjoining lands (e.g., Adventureland and Frontierland, or Old Fantasyland and Liberty Square, or New Fantasyland and Tomorrowland), and cover each pair in a half-day segment. If it's in the morning, hit the headliners in those two lands at rope drop, and then work your way back through them to complete the "anytime" attractions. If it's in the evening, make FP+ for the 3 biggest headliners in those lands, and work your way through, weaving between your FP+ reservations and the anytime attractions, and saving any headliners for which you couldn't get FP+ for the end of the night.
2 - The key to avoiding meltdowns (for you or the children!) is to preserve their usual schedule of wake-up times, bedtimes and naptimes as much as possible (perhaps until your final night, if you want to keep them up late for fireworks). My whole family leaves the parks after lunch and returns to the hotel for a good 1-2 hour nap every afternoon, and it makes all the difference in our attitudes and energy levels. Also, build plenty of bathroom/snack breaks into your schedule. Keeping everyone rested and refreshed at all times is the best way to ensure that you're all equipped to have a wonderful time, and to handle any snafus (e.g., an unexpectedly long wait for an attraction, a bus breakdown) that might arise.