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.
According to the view of the majority of the scholar the consent of the woman's guardian and the presence of two witnesses are conditions for the validity of the marriage contract because Abu Moosa Al-Ash’ari narrated that the Prophet said: “There is no marriage (i.e. no marriage is valid) except with a Wali (a guardian) and two witnesses of good character.” [Ibn Hibbaan]
Furthermore, it is a condition that the guardian of the Muslim woman be a Muslim, mature, and of sound mind. Allaah Says (what means): {The believing men and believing women are allies of one another.} [Quran 9:71].
Moreover, Ibn-Qudaamah reported from Ibn Al-Munthir that there is a consensus among the scholars that it is a condition that the guardian of the Muslim woman be Muslim.
Therefore, all the non-Muslim relatives of this woman cannot be her guardian, in which case the guardianship is transferred to the Muslim ruler or his deputy because the Prophet said: "The ruler is the guardian of the one who has no guardian." Therefore, if there is no ruler or ruler’s deputy, then a trustworthy and righteous Muslim man may be her guardian, look into her interests and conduct her marriage contract, and it is permissible for your father to be her guardian.
However, it is not permissible for a woman to marry herself off; if she does so, her marriage is void. The Prophet said: "A woman cannot be a guardian in marrying off another woman, and she cannot marry herself off." [Ibn Maajah]
Finally, our advice is that this woman should publicly declare that she has embraced Islam in order to preserve her rights and protect herself from her (non-Muslim) family.
Allaah Knows best.