It is quite common for young couples to go away for Shabbat Hanukah to their parents, and then return home on Mosa’eh Shabbat. It is clear that if a guest stays overnight in his host’s home, he is considered part of the household and thus fulfills his Misva through the host’s lighting; he simply asks the host to have him in mind when he lights. (Some guests also give the host some small change to purchase a share in the oil and wicks, but strictly speaking this is probably not necessary.) The more complex question is how the couple fulfills the Misva on Mosa’eh Shabbat. In many cases, the couple is still in the parents’ home when the parents light the Hanukah candles, and they stick around for Melaveh Malka and then go home. One might assume that since they are still guests in the parents’ home when the parents light the candles, they fulfill the Misva through the parents’ lighting, just as on Friday night. This is, indeed the ruling of Rav Yaakov Kaminetsky (1891-1986), in his Emet Le’Yaakob, and of Rav Shlomo Zalman Auerbach (1910-1995).
Hacham Ovadia Yosef, however, cites the ruling of the Mahari Katz (a contemporary of the Rama, in Poland) that the Misva of lighting depends upon where a person sleeps. And therefore Hacham Ovadia rules that even though the couple is with their parents at the time the parents light, and the parents have them in mind, they must nevertheless light the Hanukah candles when they return home. Even if they will be returning home late, nowadays one may light the Hanukah candles in the late-night hours because in any event most people light indoors. This ruling is recorded in Hazon Ovadia – Hanukah (p. 155; listen to audio recording for precise citation).
Summary: A Shabbat guest who returns home on Mosa’eh Shabbat should light the Hanukah candles at home, even if he returns home late, and he does not fulfill the Misva through his host’s lighting, even if he is still in his host’s home at the time of lighting.
