Some friends of ours went through this a few years ago. It wasn't an RV, but they bought a winter residence in a park in Florida and wanted to become Florida residents to avoid NY income taxes.
They told me they had to stay in Florida for one day more than 6 months (receiving mail). They also had to change their drivers licenses and vehicle registrations to Florida and change their voter registrations to Florida. (If I remember right, I think they had have their vehicles appraised and pay sales tax on them to register them in Florida.)
I would assume this would be true of whatever state you are planning to claim as your residence.
I think there was also something about social security direct deposit going to a bank with a Florida branch, too, but I am not sure about that.
They said nothing about doctor/dentist.