We know that if a parent wants his/her child to violate halacha, the law of Kibbud Av V'Eim does not apply. But what if the parent wants the child to not accept a chumra that the child feels very strongly about or that is widely accepted in the child's community?
There is a difference between a child keeping his own chumros, and trying to force his parents to follow that chumro.
This summary of hilchos kibud av v'em would seem to indicate that a child is forbidden from telling his parents directly that they're doing something wrong, halachically.
However, the question here cites the fact that kibud av v'em doesn't prevent any level of Torah observance for a child.
More importantly, (will try to find citation later) repeating a chumro on purpose on three different occasions, has the force of a neder. As breaking a neder is a serious Torah offense, certainly a child cannot break a neder for the purpose of kibud av v'em.
Of course, the child should do everything possible to minimize inconvenience for the parents.
In Shalom's scenario, the child could meet the father at a non-cholov yisroel restaurant, and order something pareve.
Similarly, a daughter may choose to purchase longer skirts, or shirts that better cover the neckline etc - but the daughter can't force her parents to spend more than they would normally spend on her clothing.
Rabbi Willig has a piece in Beis Yitzchak highlighting the distinction between what's done in the parent's presence (over which the parent has a lot more say) and what's not.
The Pischei Teshuva on shulchan aruch talks about if the parent says "don't say kaddish for my recently-departed spouse, it spooks me!" "Don't wear black clothes as a sign of mourning for my recently-departed spouse, it spooks me!" "I know there's some nice custom to fast Behab, but don't do it, it worries me about your health." (On one foot -- ignore them, listen, listen.) This seems to be discussing saying kaddish when the living parent is in the room; if the child happens to be saying kaddish halfway around the world, why would the living parent know?
Some of this will depend who you consult, but if the child is grown and on their own (paying for themselves, in their own space), then whether s/he drinks chalav yisrael (for instance) when he's home alone is his own business. (Now if his dad wants to meet him for lunch at a non-chalav yisrael place, that's trickier.) For the well-meaning teenager or college-age fellow who's still relying on his/her parents for support, putting aside all matters of the laws of kibbud av v'em, if your parents are asking you to keep baseline halacha, that's probably the healthiest thing.