Well, I work in Fort Lauderdale, so I don't quite have the "vacation" perspective.

I don't really think of it as being a very kid friendly vacation spot (compared with, say, Orlando), but there are definitely things to do.
I have never been but heard good things about airboat rides in the Everglades. You can see a lot of wildlife (alligators!), and I think kids would be into it. The Miami Zoo is nice, very large and spread out though (bring comfy shoes and a lot of water). Lots of nice beaches, of course. I think Miami Beach is nicer, and you're not that far away. It's not family friendly there at night, but during the day it's fun to walk around and see all the hotels and everything.
There are a lot of seedy parts of Fort Lauderdale, so just have your wits about you.
Las Olas is a nice place to walk around in the evening, nice restaurants ($$) for a night out, boring for kids, I'd think.
Sawgrass Mills (west of the city) is a HUGE outlet mall if you are interested in shopping.
Whoever recommended Boomers in Dania Beach - I would skip it. It's kind of sketchy and the big roller coaster has been closed for a long time now.
The Ft Lauderdale Museum of Discovery and Science is supposed to be excellent, I have not been.
Traffic can be heavy and kind of crazy, so give yourself plenty of time to get wherever you're going... it will probably take twice as long as you think it will. And wear a lot of sunscreen!! The sun really is brighter down here since we are so far south, and this time of year it is so easy to just torch yourself without really thinking about it.