I lived in FL for the first 30 years of my life, and know Disney like the back of my hand.
General rules: You're staying on property, so you get to make dining reservations well ahead of time. Get the kids into the character breakfasts, and also try to get a seat at the restaurant in Cinderella's Castle (it used to be King Stephan's Banquet Hall, now it's Cinderella's Royal Table or somesuch). The kids will be thrilled.
Call 407-WDW-DINE
Magic Kingdom:
--FastPass: Lets you go to an attraction and get a timed ticket (kind of like a reservation). This time of year they should not be necessary.
-- Railroad: If it's not busy, jump on! But usually it's packed when you're coming in because everyone else is coming in too, and it's the first thing you see. Jump on at Frontierland and ride all the way around and back to Frontierland.
--Main Street. Just accept that you will not be able to get the kids past Main Street without stopping. It's empty later in the day and easy to come back, but you won't be able to get past it.
-- Once past Main Street, turn LEFT and go to Adventureland, then work your way around. People tend to turn RIGHT and so Tomorrowland is packed to the gills while Adventureland is relatively empty. This time of year it probably won't be bad, but still, why fight the crowds of you don't have to?
-- At Liberty Square, make sure you go to the Hall of Presidents. Take the boat over to Tom Sawyer's Island, and let the kids have a ball. Most people see the island, but don't realize there's a ferry that takes you there. It's shady, quieter than the rest of the park, and a good midday break.
-- Fantasyland, make sure you go to Mickey's Toon Town. It's closing forever Feb 12th, it's the last chance to see it. It's pretty neat. It's a long walk back to it, or you can catch the train from Frontierland, go to ToonTown, then back to Frontierland.
--Underrated/underappreciated: Peter Pans' Flight, Jungle Cruise, Swiss Family Robinson treehouse, Tomorrowland Speedway (at their age, it's great), Tomorrowland Transit Authority.
General advice: EPCOT, MGM Studios, and Animal Kingdom: If there are any kinds of crowds, go straight to the back and work your way forward. Everyone gets caught up in the stuff when they come in the gate, and it takes 2-4 hours for appreciable numbers of people to get to the back. Even just keep going until you get past the crowd, then start doing stuff. Come back to the front on the way out and pick up what you missed.
Any questions, shoot me a PM with your email address, and we'll talk. (I don't want to post my email address here to avoid the spambots)
