The Mitzva of telling the story of the Exodus on the night of Pesach is formulated in the Torah as, "Ve'higadeta Le'bincha" – "You shall tell your son" (Shemot 13:8), and thus the primary obligation is to tell the story to one's children. Therefore, one's children should be seated near him at the Seder table. Many families have arrangements at their table that have the children seated at the end, with the guests and relatives seated closer to the father; it is proper, however, for the children to sit near the father at the Seder so that he can tell them the story of the Exodus.
Nevertheless, one fulfills the obligation to tell of the Exodus even if he does not tell the story to his children, and he simply says it to himself. When the Torah says, "Ve'higadeta le'bincha," it refers to the preferred manner of performing this Mitzva; but the basic level is fulfilled even if one tells the story to himself. Therefore, one need not make a point of spending the Seder with his father. In fact, it is customary in some places that married couples spend the first Seder with one set of parents and the second Seder with the other set. This is acceptable because the Mitzva to tell of the Exodus on the night of Pesach can be fulfilled even if one does not tell the story to his children.
Summary: The primary obligation of telling the story of the Exodus involves telling the story to one's children; therefore, children should be seated near their parents at the Seder table. Nevertheless, the Mitzva can be fulfilled even if one tells the story only to himself, and not to his children, and therefore children are not required to spend the Seder with their parents.
