Praise be to Allah.
There is nothing wrong with the woman growing her hair long and taking care of it
Letting the hair grow long and taking care of it is something with which women customarily adorn themselves. It is something permissible and there is nothing wrong with it. If your parents instruct you to cut your hair , then there are two scenarios:
The first scenario is cutting it in a manner that resembles the haircuts of men or haircuts that are adopted only by evil women . In this case, it is not permissible for them to instruct you to do that, and it is not permissible for you to obey them, because it is not permissible to obey anyone if he instructs you to disobey Allah, may He be exalted.
It was narrated from ‘Ali (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said: “There is no obedience if it involves disobedience towards Allah; obedience is only in that which is right and proper.” Narrated by al-Bukhaari (7257) and Muslim (1840), also narrated by Imam Ahmad in al-Musnad (2/318) as, “There is no obedience to any human being if it involves disobedience towards Allah.”
The second scenario is cutting it in a way that is free of the objectionable elements referred to above, meaning that it is a kind of cut that is permissible, such as if the woman has long hair, and her parents want her to cut it, either because in their view that makes her look better, or some other reason. What appears to be the case is that you do not have to obey them in that, because obedience to parents is only obligatory with regard to that which is beneficial for them. As for that in which there is no benefit for them, it is not obligatory for the child to obey them in that.
Obedience to parents in matters that do not involve disobeying Allah
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said:
The individual is obliged to obey his parents in that which does not involve disobeying Allah, even if they are evildoers. This is what appears to be the case from the general statement of Ahmad. This has to do with that which is beneficial for them and not harmful to the child. If it is difficult for him but will not harm him, it is obligatory, otherwise it is not." (Al-Fataawa al-Kubra 5/381).
However, if your parents instruct you to cut your hair in a permissible manner, and it does not look bad on you or harm you, and the most that can be said is that they are choosing for you something that you would not choose for yourself, then what we advise you to do is obey them, even if you do so reluctantly and it goes against your preferences, because obeying parents, even if it is not obligatory, is a means of pleasing them, and that in turn is a means of attaining the pleasure of Allah, may He be glorified and exalted.
It was narrated from ‘Abdullah ibn ‘Amr, that the Prophet (blessings and peace of Allah be upon him) said: “If your father is pleased with you, Allah will be pleased with you, and if your father is angry with you, Allah will be angry with you.” Narrated by at-Tirmidhi (1899); classed as saheeh by al-Albaani in Saheeh Sunan at-Tirmidhi (2/340).
Shaykh ‘Abd ar-Rahmaan as-Sa‘di (may Allah have mercy on him) said:
This hadith refers to the highest and ultimate level of righteous deeds, which is when your parents are pleased with you, for showing kindness to them will lead to attaining the pleasure of Allah, and it is a means of doing so; attaining the pleasure of Allah is the result and outcome (of pleasing your parents). Thus everything that pleases parents, of whatever is customarily recognized as kindness of all types, and using all means to please them, all comes under the heading of honouring them." (Tuhfat Quloob al-Abraar p. 216).
See also the answer to question no. 139414 .
And Allah knows best.