Is it permissible for a father to marry his daughter to a young man whom her family rejects, which might lead to the disintegration of the family?

A man marrying his daughter to someone who is compatible in religion and character is valid, and does not depend on anyone else's consent, even if the grandfather or brothers do not approve.

The father is the legal guardian of his daughter, and the compatibility that is considered is compatibility in religion, not in lineage.

This is based on the Prophet, peace and blessings be upon him, who said: "If there comes to you one whose religion and character you approve, then marry [your daughter] to him; otherwise, there will be tribulation on earth and widespread corruption."

However, if doing so would cause problems and disagreements between him and the family, and he cannot convince them to agree to accept the suitor, then it is better to forgo it to avoid discord.