“Family” definition of private space is brought up in the Mishnah
BROTHERS WHO WERE EATING AT THEIR FATHER'S TABLE BUT SLEPT IN THEIR OWN HOUSES MUST EACH CONTRIBUTE A SHARE TO THE ‘ERUB
The overall question is: does the definition of a private domain come from where one sleeps or where one eats? This is seen in a courtyard shared by several people who all are maintained by the same person:
Our Rabbis taught: Where a man has five wives who are in receipt of a maintenance allowance from their husband or five slaves who are in receipt of a maintenance allowance from their Master, R. Judah b. Bathyra permits [unrestricted movement] in the case of the wives but forbids it in the case of the slaves, while R. Judah b. Baba permits this in the case of slaves but forbids it in the case of the wives.
Said Rab, what is R. Judah b. Baba's reason? The fact that it is written in Scripture: But Daniel was in the gate of the king. (Dan. 2:49)
That is, wherever the kings servant went he was still “in the gate of the king”, that is – the king’s house.
The question of measuring Shabbat distance comes up for laborers who take their meals in the city but sleep in the fields, or students who eat in the country but sleep in the schoolhouse. They would, it was concluded, “much prefer” to have taken their meals where they slept (schoolhouse or field).