Allah ordered his Prophet ﷺ to command his wives and daughters to cover themselves up:
يَا أَيُّهَا النَّبِيُّ قُل لِّأَزْوَاجِكَ وَبَنَاتِكَ وَنِسَاءِ الْمُؤْمِنِينَ يُدْنِينَ عَلَيْهِنَّ مِن جَلَابِيبِهِنَّ ۚ ذَٰلِكَ أَدْنَىٰ أَن يُعْرَفْنَ فَلَا يُؤْذَيْنَ ۗ وَكَانَ اللَّهُ غَفُورًا رَّحِيمًا
O Prophet, tell your wives and your daughters and the women of the believers to bring down over themselves [part] of their outer garments. That is more suitable that they will be known and not be abused. And ever is Allah Forgiving and Merciful.
— Surat Al-Ahzab 33:59
It is, therefore, the duty of every parent in Islam to follow the path of the Prophet ﷺ and the command of Allah by ordering their wives and daughters to wear the ordained Islamic dress for women. This is for the good of the father, the mother, and the children:
يَا أَيُّهَا الَّذِينَ آمَنُوا قُوا أَنفُسَكُمْ وَأَهْلِيكُمْ نَارًا وَقُودُهَا النَّاسُ وَالْحِجَارَةُ عَلَيْهَا مَلَائِكَةٌ غِلَاظٌ شِدَادٌ لَّا يَعْصُونَ اللَّهَ مَا أَمَرَهُمْ وَيَفْعَلُونَ مَا يُؤْمَرُونَ
O you who have believed, protect yourselves and your families from a Fire whose fuel is people and stones, over which are [appointed] angels, harsh and severe; they do not disobey Allah in what He commands them but do what they are commanded.
— Surat At-Tahrim 66:6
When asked about the interpretation of this verse, the Prophet ﷺ explained that it meant forbidding them from what is wrong and enjoining them into what is right:
عن عمر- رضي الله عنه- قال: لمّا نزلت هذه الآية يا أَيُّهَا الَّذِينَ آمَنُوا قُوا أَنْفُسَكُمْ وَأَهْلِيكُمْ ناراً يا رسول الله نقي أنفسنا فكيف لنا بأهلينا؟ فقال: تنهونهم عمّا نهاكم الله، وتأمرونهم بما أمر الله
— NOTE: My own translation, so treat with care:
Narrated on the authority of 'Umar (May Allah be pleased with him) that he said: "When the verse 'O you who have believed, protect yourselves and your families from a Fire whose fuel is people and stones', we asked: 'O Messenger of Allah, [we know how to] protect ourselves, but how about our families?' He replied: 'By forbidding them from what Allah forbade you from, and by enjoining them to what Allah has ordered.'"
— Nadrat an-Na'īm, Vol. 9, pp. 3684 (Arabic only)
Accordingly, the scholars agreed that there is no doubt that parents are responsible for the actions of their children. They said that the protection is by mandating their obedience to the commands of Allah on themselves and their families, let the commands be of things to follow or things to avoid or to repent wrongdoings. The application includes teaching, advising, and forcing. Below are some examples of what the scholars said and how this verse should be applied:
- 'Abdullah ibn 'Abbās: "Forbid them from what is forbidden by Allah, and command them to do what is good and avoid what is evil. Teach them then discipline them; this is how you protect them from Hellfire."
- 'Ali ibn Abi Tālib said: "Teach them, then discipline them. Obey Allah's commands. Refrain from disobedience. Order your families to remember Allah for Allah to save you from Hellfire."
- Mujahid: "Fear Allah, and order your families to fear Allah, too."
- Qatādah: "Protecting them from Hellfire is by ordering them to obey Allah and to forbid them from disobeying Him, to help them attain this goal. If he sees disobedience, he should strongly restrain them, prevent them, and reprimand them."
The hierarchy of this responsibility is clearly defined in a hadith in Sahih al-Bukhāri and Sahih Muslim (which is quoted below). The father is responsible for himself as well as his wife, sons, and daughters. The wife is responsible for herself as well as the sons and daughters.
عَنِ ابْنِ عُمَرَ، عَنِ النَّبِيِّ صلى الله عليه وسلم أَنَّهُ قَالَ: أَلاَ كُلُّكُمْ رَاعٍ وَكُلُّكُمْ مَسْئُولٌ عَنْ رَعِيَّتِهِ فَالأَمِيرُ الَّذِي عَلَى النَّاسِ رَاعٍ وَهُوَ مَسْئُولٌ عَنْ رَعِيَّتِهِ وَالرَّجُلُ رَاعٍ عَلَى أَهْلِ بَيْتِهِ وَهُوَ مَسْئُولٌ عَنْهُمْ وَالْمَرْأَةُ رَاعِيَةٌ عَلَى بَيْتِ بَعْلِهَا وَوَلَدِهِ وَهِيَ مَسْئُولَةٌ عَنْهُمْ وَالْعَبْدُ رَاعٍ عَلَى مَالِ سَيِّدِهِ وَهُوَ مَسْئُولٌ عَنْهُ أَلاَ فَكُلُّكُمْ رَاعٍ وَكُلُّكُمْ مَسْئُولٌ عَنْ رَعِيَّتِهِ
It has been narrated on the authority of Ibn 'Umar that the Prophet (May peace be upon him) said: Beware. every one of you is a shepherd and every one is answerable with regard to his flock. The Caliph is a shepherd over the people and shall be questioned about his subjects (as to how he conducted their affairs). A man is a guardian over the members of his family and shall be questioned about them (as to how he looked after their physical and moral well-being). A woman is a guardian over the household of her husband and his children and shall be questioned about them (as to how she managed the household and brought up the children). A slave is a guardian of the property of his master and shall be questioned about it (as to how he safeguarded his trust). Beware, every one of you is a guardian and every one of you shall be questioned with regard to his trust.
— Sahih Muslim, Book 33, Hadith 24
Will the parents be punished for the sins that their daughter commits? Only Allah knows who will be punished for what, but they may be punished perhaps not for the sins themselves but rather for not stopping the sins as commanded above. Allah is the sole authority over who gets punished or forgiven, in what manner, and for what reasons.