The picture to hold is a room set aside so that a whole family can be in it together, children included. Everywhere else, the children might be in the way, or the room might be kept tidy for other people. Here they are not. That is the one idea behind all the uses: at home it shows up as comfort, and in a hotel or a pub it shows up as room and permission.
Two branches
家裡的放鬆空間
核心畫面最直接的樣子：房子裡那一間留給大家一起待著的房間。
noun · A2
A room in a house where the people who live there relax together — watching TV, playing games, or just sitting and talking. It is the comfortable, everyday room, the one the family actually uses most.
家庭起居室
外面替一家人留的房間
同一個想法搬到別人的地方：旅館和酒館也留一間給一家大小。差別在於，在家裡強調的是舒服，在外面強調的是「裝得下」和「進得去」。
noun · B1
A hotel room with enough beds and enough space for several people to sleep in, usually parents together with their children.
家庭房