I've been to the World over 25 times, and only 3 have NOT been during either Christmas Week, Easter Week, Thanksgiving weekend, or mid-Summer Break. Our last Christmas-New Years was 2009-2010 and we are currently hoping to go back for the same week next year possibly. Yup, crowds are crazy big, but as a family of two teachers and a school aged child who are over 900 miles away, there is NO WAY for us to go at other times. The way to beat those crowds? PLAN!! And I don't just mean make a plan for the day - track crowds, make reservations for meals that fit a good touring plan (eating at off times means less rush), stay onsite where you can get back to your room quick to escape when needed, use every EMH minute you can, and have a Plan A, Plan B, and Plan C ready.
And I understand that kids are off school, but I would think you can just pull them from school for 1-2 days and save yourself a lot of headache.
The majority of DW family visitors are staying for 5-7 days, so you are pulling kids from 3-5 days of school and in many places in the country (including the district I used to work in), if a kid missed 5 days for vacation in any given quarter, they failed quarter classes and might fail semester classes (some places are even stricter and you had better hope your kid doesn't miss any more days during that quarter for illness). That is a much larger headache than big crowds at DW.
Honestly, I would just skip it if that's my only option. It's not fun when it's that crowded not only because it's hard to move, eat, ride, and enjoy...but it's also a feisty, unhappy crowd. Everyone is on edge when the crowds are that crazy.
We have actually found that as many people are on edge, an equal number are just absolutely delighted to be there and in awe of what they are seeing around them (the parks, not the crowds). We have a lot of fun just being positive and making sure to enjoy ourselves. Are there grumpy, unhappy people, of course, but we've never been there when there aren't those people, so we just make sure we aren't those people!