Dutifulness to one's parents comes from the bondsman's correct knowledge of Allah, since there is no act of worship which will bring the person performing it more quickly to the pleasure of Allah than being dutiful to believing parents for the sake of Allah.
This is because the right of the parents is derived from the right of Allah, as long as they are both on the path of the faith and the sunnah, and do not prevent a child from obeying Allah for the sake of obedience to them, or move him from certainty to doubt, or from abstinence to the desires of this world, or call him to anything which is in opposition to faith and the sunnah. If the situation is like that, then it is an act of obedience to rebel against them, and an act of rebellion to obey them.
وَإِن جَاهَدَاكَ عَلى أَن تُشْرِكَ بِي مَا لَيْسَ لَكَ بِهِ عِلْمٌ فَلَا تُطِعْهُمَا وَصَاحِبْهُمَا فِي الدُّنْيَا مَعْرُوفًا وَاتَّبِعْ سَبِيلَ مَنْ أَنَابَ إِلَيَّ ثُمَّ إِلَيَّ مَرْجِعُكُمْ فَأُنَبِّئُكُم بِمَا كُنتُمْ تَعْمَلُونَ
As far as companionship is concerned, keep their company and be gentle with them. Endure their hardship just as they endured yours when you were young, and do not withhold from them that which Allah has made plentiful for you in the way of food and clothes. Do not turn your face away from them nor raise your voice above theirs. To respect them is part of Allah's command; speak to them in the best possible way and be kind to them. Allah will not let the reward of those who do good go to waste.