The Rebbe's guidance on honoring one's parents — and on what to do when a parent's wishes and Torah pull in different directions:
The truest honor. The deepest way to honor parents is to live each day by the Torah and bring them real Jewish satisfaction (IK 7731, 8334). Don't argue with parents; even when following one's own path within halachah, keep conflict at home to a minimum and increase care in all mitzvos, which brings greater harmony (IK 9775). Children can improve a strained relationship by speaking to their parents with respect and pleasantness (IK 6670). Where honoring parents and another important mitzvah seem to clash, look for a way to fulfill both, for example by involving the whole family (IK 6834).
Where to learn and whom to marry. The Shulchan Aruch rules — in the laws of honoring parents — that a young man should learn where his heart desires, even if his father objects, and that a son need not obey a father's objection to whom he wishes to marry (IK 2725, 8651, 9042). The same applies to drawing closer to Chassidus against a parent's objection (IK 4474). Parents should support this rather than place obstacles in the way, ideally with full consent (IK 2725, 8651). Invoking "honor your father and mother" to pull a child away from Torah study is a misuse of the mitzvah (IK 8765). A seventeen-year-old need not leave yeshiva to help support his father; the father's livelihood will not improve by interrupting the son's Torah study (IK 4648).
When a child takes on more. Parents should support a son's sincere decision to grow a beard and not undermine him because of what others will say (IK 2893, 3359). A son may pray in a more religious shul even against his father's wishes, as long as he acts respectfully and keeps the peace (IK 3854).
Keeping the family whole. In shidduchim, harmony with parents matters greatly — building a home should not come at the cost of family unity, and parents' concern comes from love (IK 10185). Family disputes should be settled properly and quickly, especially before a family simcha (IK 7688).
After a parent's passing. Put up the matzeivah without delay (IK 6032). Don't move a grave without consulting a qualified Rav (IK 8334). On visiting a parent's grave after many years (IK 9321), and on parents who could not receive a proper burial (IK 864), the Rebbe advised tzedakah and Torah study in their merit.
See also: Parenting – Discipline, warmth and setting an example; Parenting – Choosing a school or yeshiva for your child.