Is it permissible for a man to marry a woman through a judge after her family's refusal due to familial problems, given that the suitor and the woman are aware of their mutual consent and desire to marry, and what is the Shar'i (Islamic legal) ruling on this matter?

If the suitor is suitable for the woman, her father does not have the right to prevent her from marrying him. If he does so, he is considered a guardian who prevents marriage (عاضل). In this case, the woman has the right to refer the matter to the judge to marry her off, or to order her guardian to marry her off. If the guardian prevents the marriage with a valid reason, he is not considered a guardian who prevents marriage. It is advisable to strive to convince the father to agree, and to involve some prominent figures to speak with him. If he insists on refusing, the matter should be referred to the Sharia judge. If the prevention of marriage (عضل) is proven, the judge will marry her off.