The halacha is one is obligated to listen to the their father and mother (Kibud Av V’Eim). The halacha is also that once a women gets married she must listen to her husband ahead of her parents. (See Shulchan Aruch Yoreh Deah Siman 240:17 and commentary of the Shach. And Chayei Adam Klal 67:17 and footnote to Sefer Chareidim ibid. where he deals with this at length.) The husband must listen to his parents, even when it conflicts with his wife.
Married women are still obligated in Kibuv Av V’Aim, but they do not have to take the time to constantly do things for their parents, unless their husband allows it, since they are obligated to their husbands.
Also, a child (where the parents are not divorced) must listen to his father ahead of his mother, for the reason that his mother herself must listen to his father. If the parents are divorced, then the father loses his precedence since the mother is no longer his wife and is no longer obligated to him.
(See Shulchan Aruch Yoreh Deah Siman 240:14; Pischei Teshuva Yoreh Deah 240:12, Shu”t Rav Akiva Eiger Siman 68, Shu”t Noda B’Yehuda Mahadura Tinyana Even HaEzer Siman 45 and Chazon Ish Even HaEzer Siman 47 Dibur Hamaschil HaTel.)