Either state is fine with double towing, but if you get into Florida, you may get pulled over.
My experience was going down into Florida one year, pulling my 33' 5er and my Jeep Wrangler behind that. I made it down to Destin, did my weeks worth of fun, and on the wat back home, I passed through the Jacksonville area, when I got word from the local LEO while I was fueling, that if I didn't disconnect the Jeep, I would surely get a ticket when I pulled back out on the road. I disconnected, drove about 40 miles out of town and hooked it back up and drove on into my home state.