Don't listen to a national weather report. A local weather report will have a different forecast for every half county.. it's florida, storms aren't really big giant masses most of the time. It's not like home where the state or half of state will have the same storm... Central florida rain doesn't really mean it'll hit where oyu are in central florida. central florida is larger than some states. also being flat, storms that last days up north only last minutes down here. they move really quick which is why they all seem biblical. same rain, just compressed into 20 minutes instead of 2 days.
The local CBS (news6) has a lot of news in the morning, near lunch and near dinner. So if your in your resort just flip on the tv to cbs and it'll most likely be news and 10-20 minutes after turning it on you'll get a better idea of not only if it'll rain but where and when. It could be 100% chance of rain and never touch disney property or only touch the southern half (all the other parks).
http://www.clickorlando.com/weather/attractions is their weather news site for only the disney property.. There is also a video you can play on there that gets updated 4-6 times a day so you can get actual local weather on what's happening down here and what they are predicting (which btw, they aren't talking about sunday yet, just saying things like "could be wet for the afternoon")..