The rules for deducting travel expenses are found in publication 463, chapter 1. I do not think you would qualify to deduct travel, under the circumstances you describe. First, the travel would not be primarily or exclusively for business, and second, working from Florida would not be "temporary" within the meaning of the regulations. Consequently, you could not deduct travel to or lodging expenses in Florida, even if you did perform work there. I could be wrong in my interpretation, and I agree you may want to talk to an expert.
https://www.irs.gov/forms-pubs/about-publication-463
Also, any work that you perform while physically living or working in Florida (even temporarily) will be subject to Florida non-resident income tax. Since you currently live in a state without an income tax, there does not seem to be much incentive to perform any work while in Florida, unless you have a professional responsibility to keep in contact with your patients when you visit the beach or mouse world or whatever.
