As is well known, the Aseres HaDibros are written on two tablets; five are bein adam la'makom (between man and his Creator), the other five are bein adam l'chaveiro (between man and his fellow man). (I mean, of course, "man" in its classic sense of "human". I resist the politically correct "person" because then one should -- following that nonsense ad absurdum -- change the term to "perchild" or "perprogeny".) The mitzvah of kibud av v'em is (as is also well known) included in the bein adam la'makom group. That is, honoring one's parents (and in-laws and spouse's of parents, and older brothers) are part and parcel of directly serving HaShem. I say "directly", because it is more than just a polite request from your mom asking you to be nice to your annoying younger brother or sister; it's the real deal.
Part of kibud av v'em is not causing mental anguish to the parent. That, of course, is terribly tricky. What child doesn't cause mental anguish to their parent? I have a fond memory of my grandmother, alei'ha ha'shalom, giving her son -- my father, alav ha'shalom -- mussar about how his not talking to my sister was giving her agmas nefesh. "Don't worry," she said to him, "soon the draft will include girls, she'll get called away to war, and killed on the battlefield. Then you won't have to worry about not talking to her." And you wondered where I got my subtly gene; I loved my grandmother.
Suppose a Jewish doctor wants to work in a bad part of town. The question was actually asked in Eretz Yisrael, but there are plenty of places I wouldn't want my child (doctor or not) working. In fact, when my daughter was getting her MA in Special Education, she worked for six weeks in a facility for seriously disturbed children. She assured me it was safe, but I was still plenty nervous (especially when she told me the microwave was bolted down because one of the little tykes had thrown it at someone). The question boils down to whether it is a real sakana or not. If it is no more than "normal" danger, then the parent cannot stop the doctor-child from doing his job. There is, after all, a mitzvah to save Jewish lives and the mitzvah of kibud av v'em does not give the parent the right to tell the child to abrogate other mitzvos. On the other hand, if the danger is so real that the doctor's obligation itself is knocked down to "gimulus chasadim", then the issur of causing anguish to one's parents would take precedence and the doctor would need to find a safer venue.
One dimension of kibud is not contradicting one's parents. That, according to many poskim, includes actions that violate the parent's wishes -- even if nothing is said. Interestingly, that makes learning hilchos kibud av v'em at least as important for parents as for children -- no parent wants to put their child in a position of violating issurei d'oraisa. If you know a child is not going to listen, even if just because of being thoughtless, then you are going to want to avoid placing that stumbling block before him. For that reason, R' Fuerst said, he has seen many g'dolei yisrael refrain from telling their children what to do and instead say they prefer this or that.
While understanding how to honor one's parents certainly helps one to understand how to honor HaShem, the more important lesson may actually be to the parents themselves. I have a friend who calls his mother every time he feels neglected by his children. Try that next time you daven; daven to HaShem with the kavana you would like from your children when they need something from you.