Glad to hear back from you, Tara!
First, clearly, you'll spend a day at Magic Kingdom Park on the day that you've booked your meal at Chef Mickey's at Disney's Contemporary Resort, since you'll be right next door to the magic. (With one or more little ones in strollers, the commute between MK and Chef Mickey's, via monorail is a breeze!)
Other than that, focus on spending one day in each of the other parks, perhaps pairing an evening at Downtown Disney on the day that you visit Animal Kingdom.
To help keep everyone happy while touring, bring portable snacks with you, as well as a refillable cup for everyone. We like to bring a sealable, wide-mouthed cup per person, so that we can refill them with an icy-cold drink throughout the day.
In addition, get to each park as early as possible. Crowds will increase later in the day, and you could have hopped onto several attractions before many of these folks even get to the parking lot. On that note, head to Quick-Service restaurants before the crowds start to notice that they’re hungry. Eat an EARLY lunch so that you’re all ready for an early dinner, too. This will help keep everyone happy and will make it easier to find seating at mealtime.
Similarly, if hunkering down to watch a parade or other spectacle, have a snack on hand to make the wait more enjoyable. A bag of fruit snacks, a lollipop or even some popcorn can help even the littlest Guests wait patiently for a little while.
Because you have 4 days to visit the parks, I’d stay out of them entirely on 12/30 and 12/31. 1/3 and 1/4 are predicted to be far less crowded than those other days, so enjoy the parks once many Guests have gone home after New Year’s Eve / Day.
Send more questions as you think of them, Tara! I’d love to help!