As has been noted, the week between Christmas and New Years is the busiest week of the year at WDW. MK will close at capacity probably every day that week. And if it doesn't close, it will feel like it should.
Because you are not staying on property, you will be among the first group turned away if they start closing. (MK closes in phases, and the first phase is to people off property, as the parking lots close to cars coming in.) If you leave MK during the day for a break, realize that it is quite possible that you won't be allowed back in. Even if all you do is go into the parking lot to eat, you may not be able to get back through the turnstiles afterwards. Keep that in mind.
If you bring a cooler, you can bring it into the park as long as it's not a huge rolling cooler. Bring your lunch with you, store it in a locker and have a picnic at lunchtime.
Be at the park
first thing. "First thing" at MK during the week between Christmas and New Years means "early". Park opening will be at 8am, so you'll need to be there by 7:30am. If you're ten miles away, plan on at least a 40 min trip in -- between traffic, parking, tram and monorail, you'll need that long. So you're talking about leaving your house at 6:45am or so. I know it seems ridiculous, but again ... busiest week of the year.
One prior note said to avoid MK on EMH days. Not possible the week you're going, as EVERY day that week is an EMH day at MK.
Buy or borrow a WDW guide that has a list of all the rides. Find a half-dozen or so that are absolute MUST-DO rides. Plan those first. If Dumbo is among them, that should be your very first ride. At the very beginning of the day, you will have a line at Dumbo. The later the day gets, the longer the wait. What was 30 min at 8am will be 75 min by 11am. So do Dumbo first if Dumbo is a priority.
Fairies are very popular, so if your kids want to meet Tinkerbell and her friends, expect 90 min. If you don't want to wait in that line, then don't tell your kids they can meet Tink.
Have a strategy for waiting in line. Games, bubbles, snacks, something. Because you will be waiting in lots of lines. Lines for rides, shows, food, characters, souvenirs, the bathroom. Be ready for that.
Remember that there are four parks. If MK is closed, you have three other choices, so be sure to at least look at those parks in your WDW book too. You may not get into the park you want to get into, so have a Plan B.
I know it seems overwhelming, but ... that's Disney at Christmas!
