I think that the assumption that the minhag has binding force should be challenged. In general, the adherence to these minhagim causes rifts -- certainly across different groups of Jews (esp. Sephardi vs. Ashkenazi, but also across different sects or versions of Judaism). Phrased Talmudically, the issue is whether a mere custom which divides the people has binding force.
 More particularly, I assumed from the question that the minhag in question was "minor", in the sense that one's father might change practice without rabbinic consultation or decree.
With respect to "major" minhagim, many rabbinic authorities have ruled that it is permitted (and perhaps even obligatory) to do away with them, particularly if they are "foolish customs". [EDIT] For example, with regard to the eating of kitnyot on Pesach - a "major" minhag, relevant citations for doing away with a "foolish custom" include: (see original source here: Schechter.edu
Mishnah Eruvin 10:10 = BT Eruvin 101b; Ḥullin 6b-7a; Yerushalmi Pesaḥim 4:1, ed. Venice, fol. 30d; Yerushalmi Pesaḥim, ibid., fol. 30c at bottom; Tosafot on Berakhot 48a, s.v. veleit hilkheta; Responsa of the Rambam, ed. Blau, Nos. 308-310, pp. 566-578; Responsa of the Rosh 55:10, and more at the link provided, toward the bottom of the page.
The references above relate to a minhag for which there is uncertainty in the Halacha. When there is no uncertainty, the weight of the rabbinic opinion is that we are compelled to change the minhag. Where the issue is minor, all of these arguments apply a fortiori. [/Edit]
There are excellent reasons to do away with many minhagim:
- They detract from the joy of holidays and Shabbat by causing angst, annoyance, or friction
- They emphasize the insignificant at the cost to the significant (by definition, these customs are not as significant as the actual mitzvot to which they relate)
- They cause people to scoff at the commandments in general (if this custom has no purpose and is observed, then there is no reason to observe other commandments)
- They cause unnecessary divisions among Jews (and possibly families).
Against these negative outcomes, there is only one reason to observe most minhagim: the desire to preserve a custom. It seems clear that this desire cannot be dispositive.
Thus, you are neither obligated to change nor to follow the original custom (though if the question is stand vs. sit, presumably you must choose one or the other or begin to lie down). In your own life, the minhagim should have no bearing - make up your own mind just as your father will make up his - you too may change a minhag because you learned something, etc. When in your father's (or anyone else's house), the minhag has no power to affect the mitzvah, so broadly invoke shalom beto, go along with whatever the people do there.