If the family are living/sleeping here temporarily and this has caused an increased amount of traffic in an otherwise relatively quiet estate, you bet your ass they're aware of the parking, or lack thereof, as they themselves will encounter difficulties in wherever they park their own cars. (If it was my family, I'd have gone out of my way to make sure the nurse had parking - I'd move my own car somewhere else and let the nurse park in the drive, if required........an ill member of the household does not give you a free pass to act the dick).
I'm sure they have a load on their plate, but bottom line is OP's mam should have been consulted and her permission requested before someone plonked their motor in her feckin driveway.
Where the nurse parked is not on the list of concerns.
The nurse knows, or should know, that she/he has to make their own arrangements.