Does our golf group have to be associated with a single golf course, as a “home club?”

No, the group/club does not have to be associated with a single golf course. The majority of clubs actually play golf at a variety of facilities. The “home” for a club may be a place that members congregate for other functions, the house of a club official, almost anywhere. We happen to call groups that are not tied to a single golf course “affiliate clubs.”