Is a marriage contracted verbally between the guardian of the girl and the prospective husband's paternal uncle (who acted on behalf of his son), without official documentation, considered valid, and is it incumbent upon the girl to resort to the court to seek divorce after her husband (her paternal cousin) refused it, knowing that the dowry was not paid and the husband married another woman and left her in limbo?

We understand that your paternal uncle undertook both sides of your marriage contract. If he was your guardian due to the absence of closer relatives, and with his son's authorization to him, then scholars have differed on the validity of this. An independent dwelling is the right of the wife, so she has the right to refuse mixed living arrangements. She also has the right to refuse to surrender herself to her husband if he has not delivered her Mahr (dowry). The husband's refusal to divorce or khul' (a form of divorce initiated by the wife) is harmful to her. You should refer to the Sharia court to rule on the validity of the contract and to compel the husband to divorce, or for the judge to issue the divorce.