Ask Mr. Smarty Plants

Calyptocarpus vialis (Horseherb or Straggler Daisy) is a mighty fine ground cover. It will grow in sun, partial, and full shade, and needs no mowing unless you want the exercise. [Maybe just a light shearing if it gets too straggly] It establishes itself quite readily, and is adaptable to the kind of conditions you describe.

       
Calyptocarpus vialis                       Calyptocarpus vialis

 There are web/book references to this being a native from the Keys to Georgia so it ought to do just fine in Ft. Lauderdale.  You can see on the distribution map on the USDA Plant Database that this plant grows in Florida.  If you click on Florida on the map, you will be able to see that it grows in Broward County. 

There are, of course,  several other possible plants you might consider.  One might be Sesuvium portulacastrum (Shoreline seapurslane).  It is low and trailing and wouldn't even require any mowing, etc.    Ipomoea pes-caprae (Railroad vine) is another low, drought tolerant groundcover.   Another on their list is Lippia nodiflora.  This is a synonym of Phyla nodiflora (Texas frogfruit).

             
Sesuvium portulacastrum               Ipomoea pes-caprae                    Phyla nodiflora

If you REALLY want to get into a search for Florida groundcovers - the The Institute of Food and Agricultural Sciences (IFAS) of the University of Florida has a great analysis and shows you several other options.   The Native Plant Society of Florida also has a recommended website for Florida native plants. In particular, they have recommended lists of native plants, including ground covers, for all the different areas of Florida.  Click here for the list for Broward County.  I encourage you to look into these websites for more information.