Does the obligation of Hijab fall away from a girl if her family prevents her from it, and one of them threatens to leave the house if she wears it, knowing that the intended Hijab is only covering the hair? And what should she do?

The aforementioned girl must take the initiative to wear the hijab in obedience to Allah, and not abandon it to please anyone, for pleasing Allah is more important. Her displaying of her adornments (tabarruj) is one of the major sins. She must speak to her family kindly and explain to them that this is Allah's law, and that happiness lies in obeying it. She must be patient with any harm she faces for adhering to her religion, for Allah is with her with His help and success if her intention is sincere.