AP Psych - Is this considered by UF, USF, UCF & FSU as part of the recalculated GPA?
Probably, as it is an academic course in the social sciences. HOWEVER, no one but the Admissions Offices (and probably your HS counselor as you live in Florida,) can say for certain if it will. IMO, your kid should take it even if it’s not counted: it’s an extremely interesting and relatively low-work class (especially if taught as a full-year, given that it typically corresponds to a one semester course,) the AP credit could potentially count towards general education requirements, and it’ll impact your worldview of how and why we, as humans, behave the way we do. High school’s one of the best times to explore other areas, especially because you don’t have to juggle degree requirements and paying for individual courses as in college. 
https://registrar.fsu.edu/bulletin/undergraduate/information/admissions/ says:
https://www.ucf.edu/admissions/undergraduate/faq/freshman/ says something similar.
https://questions.ufl.edu/faq/how-will-uf-compute-my-high-school-gpa/ is somewhat more vague.
Psychology is generally considered a social science course. You can ask the admissions offices to be sure.
My twins are doing FLVS FLEX this year due to the Pandemic and we don’t have a good counselor. The one at FLVS doesn’t know enough to be of assistance. I’m the guidance counselor, principal and teacher this year. I have seen posts here saying that virtually all AP classes are recalculated and considered as part of the GPA, but the school websites say otherwise. I’m confused.
Contact the Admissions Office at each school, as they’re the ones with the final say on anything Admissions-related (colleges usually won’t approve individual course schedules, but they’ll be more than happy to point you in the right direction about GPA–that’s why they’re there!)
Hope that helps!
It is part of the recalculation.
-School counselor in Florida
Also I highly recommend getting a copy of the SUS matrix. It’s super helpful
Use this handbook link for what courses count as core.
https://dlss.flvc.org/c/document_library/get_file?uuid=fef3eba1-9c6b-a229-ab92-0aba1bce0080#page=60
Here is what I know
UF - .5 for core honors and 1.0 for ALL AP/IB AICE* and 1.0 for Dual Enroll CORE ONLY
FSU - .5 for core honors, 1.0 for ALL AP/IB/AICE* and 1.0 for ALL DUAL ENROLLMENT
UCF - .5 for Core Honors, 1.0 for CORE AP/IB/AICE*. Unsure about Dual
- C or higher