Non-commercial double tow is NOT legal in Florida, no matter what your home state allows. This is not often enforced, but it could be if the LEO decides to target you. You can be required to drop the second trailer on the spot and then pay a towing company to get it out of their yard. Not cheap!
Commercial carriers must have a special permit and the roads and routes they can use are severely restricted. (Usually limited access highways and within 2.5 miles of an interchange on surface streets.)
This is based on 24 years at Orange County Public Works, most of it as the Traffic Operations Engineer, including coordination with commercial carriers requesting permits from DOT.
See Florida Statutes Chapter 316 and plug "double tow" in the search box.