I went on a villa holiday to Florida a couple of years ago. There are some companies that will arrange villas for you, but it tends to be cheaper and you're more likely to get what you want if you hire a specific villa from the owners through a third party company, for the peace of mind. A good place to start looking for villas is on OrlandoVillas.com.
In particular I can recommend Villa Gardenia which is where we stayed, though that was for 6 people rather than 4. We found the location was excellent for access to the various parks, while remaining in a relatively fairly quiet area with no planes going overhead. There were various supermarkets and other useful shops just a short drive away.
Try and work out in advance what parks you want to go to and book your tickets before you leave the country. You can get much better deals that way. The Disney parks are fantastic but will always be manic, we found the quieter SeaWorld with equally as good rides much more enjoyable.
Definitely get to the parks early, with tickets in hand, because the best time to run round and do all the rides is first thing. For Disney parks in particular, we were at the parks for opening time to do the rides, headed home for lunch and the heat of the day, then went back late afternoon/evening for the various shows.
If you want to go to the seaside, Siesta Key is a fantastic beach that makes a good day-trip out to the West Coast. Warm sea, sandy beaches, lots of free parking and excellent facilities - free toilets and showers kept spotlessly clean.