We've met a number of full-timers who use a relative's address (kid, sibling, etc.) as their legal domicile. None of them have mentioned any issues. I'm sure there are differences among the states, though, so you might want to seek some expert advice about Florida specifically. The main aspects are drivers' licenses, vehicle registration, income taxes, voter registration, and your banking institution(s). The Escapees RV Club has a lot of information on this on their main web site.
Rob
U.S. Army retired
2020 Solitude 310GK-R
MORryde IS, disc brakes, solar, DP windows
(Previously in a Reflection 337RLS)
2012 F350 CC DRW Lariat 6.7
Full-time since 8/2015