What is the Sharia solution for this girl whose family refuses her marriage, though her marriage contract has been solemnized, and her father threatens to divorce her mother if she insists on completing the marriage, so would her going with her husband be considered disobedience to her parents, knowing that she fears for her mother from her father's threats?

First: Turn to Allah with supplication, humility, and ask Him to facilitate convincing your parents.

Second: If the religious marriage contract has been concluded and the dowry paid, she has become a wife, and there is no justification for refusing to complete the marriage.

Third: Seek help from people of virtue and wisdom for advice, and if that does not work, the matter can be taken to the Sharia court.

Fourth: Completing the marriage is not considered disobedience to your parents, but strive to gain their رضا (رضا - approval/satisfaction).

Fifth: What the father is doing—coldness and threatening divorce because of the marriage—is ill-treatment, and obedience to parents in separating from one's husband is not obligatory.