How can the aforementioned girl stop making mistakes and repent, when she cannot reach a solution in her marriage?

A Muslim must realize that this world is a transient abode, not a permanent dwelling, and that it is not worth a gnat's wing in the sight of Allah, and that it is a means to the Hereafter. He must fear Allah and be mindful of Him in his actions. As for the inability to engage in marital intimacy, it is the wife's right, according to Islamic law, to take her case to the judge. If a mutual agreement for divorce is reached without resorting to the judiciary, there is no harm. The wife must sever every relationship that is displeasing to Allah.