Room with living room: a room to retreat to, as from a restaurant, where retreat means to retreat or leave, especially to a quiet or private place, especially to a quiet or private place.
So the meaning of checking out can basically be understood as a private lounge.
The translation of the full text can be:
The retreat room is a relatively private room, and only the owner, his wife or very distinguished guests (who now live in a room in the apartment) can "relax".
It refers to the owner of the house, his wife or a distinguished guest living in one of the main apartments of the house.
Let me give you an example: the twins are so alike that I can't tell who is who.
It can refer to (those people), and it is not necessary to use to who or who to refer to those people. I am not a teacher. When your teacher makes a mistake, she can translate and ask you here! Teachers make more mistakes than non-teachers.
For your reference!