One of the most important wajib acts that has been mentioned in the Quran after believing in one god and rejecting paganism is honoring, respecting and obeying parents. In respect to the cases that the order of each of the parents contradicts the order of the other in a way that the child can not carry out both, we come across two groups of Ahadith. Some of the Ahadith say that respecting and obeying the mother has precedence while other Ahadith say that the child is more indebted to his father than any one else (and therefore he would have to carry out the order of his father). Therefore it seems that we can reconcile between both Ahadith and explain the matter in this way: Regarding the issues that there is a right for the father to intervene, like the right of getting married for a virgin girl and etc, then the father's order must be carried out, but regarding the other issues the mother's order should be carried out.
In the Quran after forbidding people from paganism the Almighty has asked for the respecting and obeying of parents. The late Allamah Tabatabei says: "After the belief in the one god, respecting and obeying parents is one of the greatest wajib acts and there is no difference whether the parents are believers or disbelievers in terms of being obeyed and respected; because the Quran has mentioned doing good to parents and respecting them in a unconditional form: "you shall be good to the parents".
Regarding your question one must say:
A: Some times the mother and father are both ordering their child to do a prohibited act. In this case obeying neither of them is wajib.
In this respect the Quran says: "We have enjoined man to be good to his parents. But if they are (Mushriks) and urge you to ascribe to Me as partner that of which you have no knowledge, then do not obey them."!
Imam Ali says: "Obeying the created is not accepted when it is a way of disobeying the creator".
The Imam also says: "It is the right of the father to be obeyed in every issue except for what is considered disobeying Allah."
In this regard Imam Reza says: "Doing good to parents is wajib, even if they are Mushriks (Pagans), but if they order their child to commit a sin then they must not be obeyed."
But if they are not commanding the child to commit a Haram act, like asking him to do a Mustahab, Makrooh or Mubah act then he must obey them, and this accounts for the fatwas the ulema have issued in this regard:
1- If a mother or father have forbidden there child from doing mustahab fasting, then it is an obligatory precaution not to fast, also if the mustahab fasting of a child bothers his parents then he must not fast, and if he has started fasting he must break it.
2- If a mother or father order their child to pray jama'ah, since obeying the mother and father is wajib, as an obligatory caution he must pray jama'a with the intention of istihbab (being mustahabb).
3- Praying at the beginning of prayer time is mustahab, but if a father orders his child to do a mustahab or Mubah act at the beginning of prayer time, then the child must carry out their order before praying at that time.
B: In some cases one of the parents orders the child to do an act that is not haram while the other parent orders the child to do a haram act, in this situation it is obvious that the child should definitely carry out the order which is not haram.
C: Sometimes both parents order the child regarding the same issue, but one of them is ordering him not to do this act while the other parent is ordering him to do this act.
In respect to these situations one must say that regarding the issues which there is a right for the father to intervene, like the right of getting married for a virgin girl and the like, then it is quite obvious that his order must be carried out. But regarding the issues which no right has been allocated for neither of the parents there are two opinions mentioned in the Ahadith.
On one hand it has been narrated from the prophet in the hadith records that a man came to the prophet and said: "Who should I do good to?" The prophet responded: "[Do good] to your mother". The man repeated his question. Once again the prophet responded: "[Do good] to your mother". For the third time the man asked the same question and for the third time the prophet responded: "[Do good] to your mother". When the man mentioned the same question for the fourth time the prophet responded: "[Do good] to your father".
On the other hand it has been mentioned in many Ahadith that the prophet was asked: "Who is a person mostly indebted to?" The prophet responded: "He is most indebted to his father."
There is also another hadith in which the prophet says: "You and whatever which you own are for your father."
Regarding the explanation that would reconcile between these two types of Ahadith one must say that almost all Ulema agree that the parents should be obeyed about things that aren't haram. It is also understood from the Ahadith that in such situations the child must show more care and obedience to his mother.
The Ahadith that back this opinion are as follows:
1- As we mentioned before the prophet advised the Arab man to do good and care for his mother for three times and in the fourth time he advised him to do good to his father.
2- Although the hadith mentioned earlier indicates that the child is most indebted to his father, but other Ahadith clearly say that the child is more indebted to his mother. For example the prophet was asked: "What is the right of a father?" He responded: "He has the right to be obeyed until he is alive." Then he was asked: "What is the right of a mother?" He responded: "How far-fetched, how far-fetched?! If you do good to your mother so many times that the number exceeds the number of the sands of the deserts and the number of raindrops it will not make up for even one day that you were in her womb."
3- Mothers have more sensitive feelings and such a character needs more care and therefore obeying the mother’s order is in accordance with the nature of women.
At the same time it is noteworthy that in such situations the child must try to choose a way to obey his mother that will entail less inconvenience for the father.
 Tabatabai, Mohammad Hosein, (Farsi) Translation of Al-Mizan, vol. 13, verses14 and 23 of surah Isra.
 An’am:151. Also, there is a hadith by Imam Baqir (as) that reads: “Do good to your parents, let them be good or bad” Biharul-Anwar, vol. 71, pg. 56.
 Ankabut:8; Luqman:15. Of course the verse goes on to order us to keep their company honorably in this world.
 “لا طاعة لمخلوق فی معصیة الخالق” Nahjul-Balaghah, saying 165.
 " اِنَّ لِلْوالِدِ عَلَی الْوَلَدِ حَقّاً … فَحَقُّ الْوالِدِ اَنْ یُطیعَهُ فی کُلِّ شَیْءٍ اِلّا فی مَعْصِیَةِ " Nahjul-Balaghah, saying 399.
 Majlisi, Biharul-Anwar, vol. 71, pg. 72.
 Tawdihul-Masael (annotated by Imam Khomeini), vol. 1, pg. 966, issue 1741.
 Tawdihul-Masael (annotated by Imam Khomeini), vol. 1, pg. 769, issue 1406.
 The First Shahid says in his book Qawa’id: There is no doubt that things that might be wajib or haram about others, are wajib when it comes to parents. Special rulings apply to parents, namely:
a) Mubah or Mustahabb travel without their consent is haram
b) Obeying them is wajib at all times, even in cases of precaution, because these cases are mustahabb, while their obedience is wajib.
c) If they call him and it is the time for prayer, he should delay the prayer and answer them.
d) If they forbid him from participating in jama’ah prayers, the verdict that seems righter is that he doesn’t have to comply, unless doing so brings about hardship for them, like if he goes in the darkness of the night for the isha or fajr prayer.
e) In the case of jihad being wajib kifayi (a wajib that is wajib upon all unless the needed number take care of the task), they can forbid him from going.
f) If the father isn't content, his child cannot fast mustahabb fasts. Al-Qawa’id wal-Fawa’id, vol. 2, pp. 47-49.
 See: Wasa’ilul-Shia, vol. 14, pp. 11-120.
 Majlisi, Biharul-Anwar, vol. 71; Kafi, vol. 2, pg. 159.
 Sheikh Hurr Ameli, Wasa’ilul-Shia, vol. 14, pg. 112, hadith 253000, “مَنْ أَعْظَمُ النَّاسِ حَقّاً عَلَى الرَّجُلِ قَالَ وَالِدُه”.
 Saduq, Ma’anil-Akhbar, vol. 1, pg. 257.
 Of course one must pay attention that there have been discussions by the ulema regarding the obedience of parents being wajib or bothering them being haram. Some of them propose that obedience isn't wajib, but bothering them is haram. They say anything that bothers them should be abstained from, unless it is a wajib act, and if he really wants to do it, he should hide it from them so they don’t get bothered or somehow draw their consent first. So obeying them isn't wajib per se (they just don’t have to be bothered). Tabrizi, Jawad, Estefta’ate Jadid, issue 2230; Mohammad Fazel, Jame’ul-Masa’el, vol. 1, issue 2188; Imam Khomeini, Tawdihul-Masa’el of the maraje’, vol. 2, unrelated issues (masa’el mutafarriqah), issue 85, pg. 675.
 See: Mirza Qummi, Jame’ul-Shattat fi Ajwibatil-So’alat, vol. 1, pg. 241. He says: “Anytime one is stuck between the orders of his mother an father in a way that both orders can't be obeyed at the same time, it isn't unlikely that the mother’s has precedence.”
 “قِیلَ یَا رَسُولَ اللَّهِ مَا حَقُّ الْوَالِدِ قَالَ أَنْ تُطِیعَهُ مَا عَاشَ فَقِیلَ مَا حَقُّ الْوَالِدَةِ فَقَالَ هَیْهَاتَ هَیْهَاتَ لَوْ أَنَّهُ عَدَدَ رَمْلِ عَالِجٍ وَ قَطْرِ الْمَطَرِ أَیَّامَ الدُّنْیَا قَامَ بَیْنَ یَدَیْهَا مَا عَدَلَ ذَلِکَ یَوْمَ حَمَلَتْهُ فِی بَطْنِهَا”, Mustadrakul-Wasa’el, vol. 15, pg. 204, hadiths 18014-18019.