Suppose a parent feels very strongly against a certain aspect of halacha, for whatever reason. What would be an appropriate way to follow halacha while maintaining kibbud av v'eim?
I'm going to echo Menachem's answer but go one step further. I have learned on many occasions that it isn't that one is required to follow Halachah despite the apparent conflict with Kibbud Av VaEim. It is, rather, that there is no Kibbud in this case. In other words, it's not a conflict. The instant that a parent's desires rise to conflict with a point of Halachah, the requirement for Kibbud falls away.
Having said that, I understand your desire not to upset your parents in any case, and my advice would be to explain to them that [Halachah X] is just what we do, and that you hope they will respect your choices.
If his father told him to transgress one of the words of the Torah, whether a positive commandment or a negative commandment, or even something from the words of [Chazal], he can't listen to him. Yoreh Deah 240:15.
However, if he sees his father transgress something, he shouldn't say "You transgressed," but he should say "It says such-and-such in the Torah" (above, 11)
Vayikra 19:3 states:
From the juxtaposition of the two clauses in the verse, the Talmud (Baba Metzia 32A) learns out that one is not required to honor one's parents if they demand he transgress G-d's commandments.
[in other words, they learn the verse like this: One must fear (and honor) his parents. Just like that is a commandment from G-d, so too is keeping Shabbat (i.e. the other commandments). Honoring one's parents does not trump other commandments. If they want you to transgress other commandments, you are not required to listen.]
This is the source for the Halacha brought in @ba's answer.
I'm not sure I understand your question. Are you asking "am I obligated to honor my parents", or "what's the best way to blow them off without blowing them off?"
The example you give -- mechitza at a wedding -- is a practical and halachic preference but you'd be hard-pressed to explain why it's "required." (Men not dancing with women? Obligation according to everyone. Men not sitting with women? Depends who you ask. Having a partition up? Good idea to prevent gawking but I don't know if anyone requires it.)
In short: it depends.
How wrong? If a parent orders you to violate a clear-cut commandment, whether Biblical or rabbinic, whether by commission or omission, then you ignore your parent.
But there can be things of positive value that aren't absolute commandments. (See Pischei Teshuva discussing a series of this in Yoreh Deah.) For instance: Bob's mother died, so Bob is saying Kaddish in shul. Bob's father Tom hears Bob saying kaddish and gets the heebiejeebies, reminded of his own mortality. Tom orders Bob not to say kaddish. -- In this case, it's debated in the Achronim but we rule that Kaddish, while technically post-Talmudic and therefore post-rabbinic, is strong enough to override parental wishes. If, however, Tom says "Bob don't wear mourning colors!", Bob should acquiesce.
So if you go to a rabbi who believes, for instance, that ordinary milk sold in the USA is downright rabbinically prohibited and say "my parents want me to drink this", he'll tell your parents to go jump in a lake. (Because, um, well, if they go to mikva more often it will make them more spiritually attuned to the horribly destructive effects that chalav stam has on your neshama.) If the rabbi holds it's a halachic preference but not requirement, then the pros and cons get weighed.
How broad is the obligation to obey? Maharik says anything not directly affecting the basic physical needs of the parent isn't included. (Therefore, according to Maharik, a parent who says "don't marry her" has no standing for his request whatsoever.) As I understand it, Rabbi Hershel Schachter shlit'a leans towards this view. Yet many others say a parent can ask for all sorts of things that are tangentially beneficial. (Rabbi Mordechai Willig shlit'a describes the Chazon Ish is a "maximalist", which is Rabbi Willig's approach as well.)
Limitations. Chazon Ish writes that one is only obligated to accommodate a reasonable request; beyond that, "the parent is obligated to cancel his request." For instance a parent can't demand all of a child's money.
So what's practically recommended will vary from case to case.
In the situation where there's no gray, e.g. "I want shrimp served at this wedding", then philosophically our approach is that we can honor people without necessarily obeying them.