Best time of year for FL is March-April-May. Best weather by far, but Americans also know this!
If you do go, make some time for a trip to the Space Coast/Merritt Island/Cocoa Beach. It is a quick hours drive down the Tollway. The beach is beautiful, it is more "old Florida" if getting more commercialized than ever. Cape Canaveral is a great day out IF your kids have any interest. If not, spend the day at the beach! I run into Ron Jon Surf Shop t-shirts all over the world from people who went to Disney, but took time to go to one of the nicest stretches of beach in that area of FL.
If you can afford it, find the BEST PACKAGE DEAL you can to stay on the Disney property. If you have a big family and that gets too expensive, a VRBO deal may be your best bet, but you will need transport to Disney.
Good luck and hope you can get the family over here. It will be a great experience for your kids and they will talk about it forever. Spend an extra quid and it will come back to you many times over, year after year.