I'm translating a text about accommodation in Croatia where a lot of families rent out their apartments or houses. Which expression would be better for this type of private business: private accommodation or family accommodation?
I'm not sure that either term would automatically make an AE speaker think of a vacation sublet.
We call them "vacation rentals" because companies who own apartments and houses also rent them, as well as individual owners, and the "family" part would be determined by the described size of the property in the listing. For instance, it's possible to sublet (or AirBnB) a small studio apartment, but that would not be a "family accommodation" since it's usually only useable by one or two people.
Edited to add: I have seen "Private room" for vacation sublet in cases where it's a room in a larger space occupied by others, like occupying one bedroom of a three bedroom apartment with some agreement as to usage of the common areas.