What should a girl do when she is willing to wear the Hijab but her parents say that she can't wear one or she can have the option of wearing one after she gets married?
as salam alaikum
you should always respect your parents and treat them kindly. However they cannot dictate the way you have to live your religion. A hadith says:
لا طاعة لمخلوق في معصية الخالق
"There is no way to obey a creature by disobeying the Creator" (see "Musnad al-Imam al-Kazim").
You should also try to guide them with good manners and give them nasihah concerning their religious duty as Muslims and parents.
With prayers for your success.