Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.1030 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)
Other (non-Avios-earning) options for getting from WAS to Florida include one-way car rental (which can be quite inexpensive at certain times of the year), and Amtrak's Silver Star and Silver Meteor services which run daily from Washington's Union Station to both Orlando and Kissimmee. Sleepers on the train will be pricey, but if you have -- or can get -- Amtrak Guest Rewards points or Chase Ultimate Rewards points (which can be converted to Amtrak Guest Rewards points), you can book two roomettes for a total of 30,000 points. Meals are included.
Both driving and taking the train will kill a day, but might be worthwhile if the family would enjoy the experience.