If a person goes to visit a resident in a Florida healthcare facility can the facility demand to hold the persons drivers license until they leave?
Yes, they can. They can in fact entirely bar entry into their facility, require that you put down a damage deposit, or various other things. If the legislature wanted to, it could pass a law that prohibits a facility of some type from restricting access to the facility in a particular way (such as barring the common requirement to check in and check out); it is likely that the owners would successfully argue that such a law is not constitutional. There is no such law in Florida, so they can require you to check in and out, they can require you to show ID, and they can require you to surrender your ID in order to get compliance with the check-out requirement.