What is the ruling of Islamic law regarding the aforementioned behavior, which involves a father refusing to marry off his daughter to a young man of good character and religious commitment, given that the reason for the refusal is previous disagreements with the young man's father, and that the girl is being subjected to violence by her father to compel her to marry someone she does not desire, and is it permissible for the young man and woman to elope together if the refusal continues?

If the rejection is due to animosity between the parents, then the husband is mistaken, and it is not permissible for him to force his daughter. Efforts should be made to reconcile the parents. If that is not possible, it is better to disregard this marriage and seek another wife. Resorting to the judiciary is possible if the guardian is preventing the marriage without just cause, but it is not encouraged except out of necessity due to the potential tension it might cause. According to the Hanafi school of thought, it is not permissible for a guardian to force his daughter to marry someone she does not desire, while the majority view permits forcing a virgin. It is not permissible to elope with a woman without a marriage contract. It must also be noted that a paternal cousin is a non-mahram, and it is not permissible to discuss matters of love and infatuation with her.