All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
Claiming that the ruling of Hijab is not mentioned in the Qur'an is totally baseless and proves the ignorance of the claimer. Allaah says (which means): {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 Allaah Forgiving and Merciful.}[33:59] Allaah further says (which means): {...and not expose their adornment except that which [necessarily] appears thereof...}[24:31]. The verses of the Qur'an and the Prophetic narrations that oblige wearing Hijab and covering the body and which dispraise unveiling are abundant. To know the evidences that prove the obligation of wearing Hijab read our Fatwa: 83033.
The family of this girl should have been thankful to Allaah for the steadfastness of their daughter and her adherence to the religion instead of mocking her. Muslims should know that mocking the rites and rulings of Islamic legislations may lead them to disbelief. Allaah says in this regard (which means): {...Say, "Is it Allaah and His verses and his Messenger that you were mocking?" Make no excuse; you have disbelieved [i.e. rejected faith [after you belief...}[9:65-66]. Thus, they have to repent sincerely and must cooperate with their daughter/sister to be obedient to the Lord and must avoid becoming a tool in the hands of Satan by mocking her or harassing her.
As for you sister, we advise you to be patient, persevere to attain Allaah's reward and do not give in if they want you to disobey your Lord. Do not be discouraged by their mocking and remember the saying of Allaah to His beloved Messenger which means: {So be patient. Indeed, the promise of Allah is truth. And let them not disquiet you who are not certain [in faith]}[30:60]. Try to convince them and to call them to the truth by such means as good booklets, Islamic cassettes that contain impressive lectures and by introducing them to pious people, etc. Overall, you have to be wise in your actions and dispositions especially with your parents.
Allaah knows best.