A few quotes from the Rabbi on 'Traditions of the Fathers'
in which he bases his ruling concerning a father who eats in his son's home on customs applying to a son supported by his father.
Question: A property owner owns two houses, one in which he studies during the day and in which he sleeps at night, but has his evening meals in his other house, where his married son, whom he [financially] supports, sleeps. After eating, he returns to the house in which he studies during the day. Must he light Hanukkah candles in both houses, or does [lighting] in one house, where he eats with his household, suffice. Also, must a married son who is supported by his father, and has a particular room in which to sleep, light [candles] himself or not.
Reply: The TOR [Ba'al HaTurim, Rabbi Jacob ben Asher] wrote in the following words in section 777: My master, my father, the ROSH [Rabbi Asher ben Jehiel], of blessed memory, in a response: A son who eats at his father's or at his friend's and has a special house in which to sleep must light, since as he has a particular house in which to sleep and the world sees him enter and leave it, there risk exists that if he does not light, that the world does not know that he eats in another place… What is implied by that which is written is that a son who is supported by his father - even if he is married, even if he wishes to light in the room in which he sleeps, it seems simple to me that he may not recite the blessing unless he himself wishes to light - depends on his father's [reciting the] blessing. And this all applies in the case that he wishes to light so as enhance the commandment, for the principle of the law, in my humble opinion, it suffices that he participate with his father with a few pennies worth and he needn't at all light in his room, since in our times we actually light inside, and even more certainly so in our city, where everybody knows that he eats together with his father. Anyhow, concerning our case – a father who eats in his son's home and sleeps in another room need light only in the room in which he eats with his son, and all this applies when the son is married, for if he is not married, he need not even participate with a few pennies.
Chessed LeAvraham, Part 1, Orakh Haim, paragraph A, Bezalel Halevy Ashkenazi Press, p. 22a – 23a, Salonika, 1813