I've lived in Florida many years and while it can possibly happen, all day rains this time of year (except during hurricanes) are not anywhere near as common as the standard Florida flood and flicker (what I call them). We sometimes chuckle a bit at the people who would automatically assume that when these storms come up, that they are day breakers. Not hard to see why someone would think that. They are usually accompanied with dark sinister clouds, lots of lighting and lots of rain that appears to be the whole horizon with no end in sight. However, these are misleading and usually they only last between 20 and 40 minutes. They are also almost always in the afternoon between 1-4pm with a light sprinkle sometimes at night. In fact, I often wonder why we need a weatherman here in the summer, when the forecast is usually, "It's going to be partly cloudy with afternoon to evening thundershowers. Highs in the low to mid 90's and lows in the mid 60's." The thunderstorms are a daily event, more they will than they won't.
As I suggest to most tourists, just find yourself an attraction, preferably a long one, or a restaurant where you can feed or entertain yourself and your family for that time, and you'll be fine and hopefully the rain will have cooled everything down.
One point though, some outdoor shows (most notably the Castle Forecourt show, are subject to certain rain restrictions. The Castle one does not have further shows after a 20 minute rain session, due to the stage surface being too slippery to dance on and are generally cancelled for the remainder of the day. So you might want to see it early if that is your plan. Other shows are usually either rescheduled, may skip a single performance, or may do a minimized performance (less dancing or action) during rain.
Water parks may or may not close for the remainder of the day depending on the storm and intensity and time of day. Sometimes they will give refunds or tickets for another day (if you paid for a day pass) depending on what time and how long you been there.