The Halacha discusses how a guest should fulfil the Misva of Hanukah lighting in his host's home. In general, the guest should participate in the cost of the wicks and oil of his host by giving him a coin and thereby become a partner in his lighting. The most common case today is when married children spend a few days in their parent's home during Hanukah. Is this also considered a classic case of a guest, in which they must share the expense of their parent's Menorah lighting. Hacham Ovadia rules that since the children are being hosted in every aspect- sleeping, eating etc. they are not considered guest, but rather members of the family. Therefore, they do not have to make a monetary arrangement with the head of the household.
Hacham Bension concurs with this, based on the opinion of the GInat Veradim (Rabbi Avraham Ha-Levi, Egypt) who holds that the Halacha of a guest applies only to instances in which the guest is paying for his room and board; that is why he must also pay for participating in the Hanukah light. Nevertheless, Hacham Bension holds that it is praiseworthy to take the stricter opinions into account and give the host a coin to participate.
If the guests are a family, it is sufficient that just the father gives money to participate in the Misva. If he would light for himself, everyone else would be subsumed under him, so too they are included in his monetary participation.
It is not necessary for the head of the household to add extra oil on behalf of the guests who gave him money, although the Mishna Berura cites opinions that do require it, and that is also the opinion of the Kaf HaHaim (Yaakob Haim Sofer, 1870-1939 Jerusalem). In any event, the money given only designates a small portion of the oil for the guest. He is not buying the entire cup, or even half of it.
Married children visiting their parents on Hanukah are not required to give them money to participate in the lighting, although it is praiseworthy to do so.