There are plenty of legal, fully insured and licenced private taxis, mostly Merc vans & exec saloons etc., they have the "SP" badge on them, which OK, stands for "servicio público", but these are distinct from the white taxis that use the ranks. They are pre-booked, which sounds like private hire to me. Like I said, they mostly advertise as airport transfers, but they'll take you to-from anywhere you want. However, they are unlikely to be particularly interested in running the OP & his parents around Marbella to restaurants unless they're willing ot pay for a VIP service. Hence my suggestion that he just uses local public taxis.
The "so called" private hire that you mention are run by people like Our Tony down the pub, and naturally should be avoided. If they don't have the "SP" badge on them, they're illegal and uninsured.