What is the ruling on a father refusing his son's marriage to a girl he loves, and compelling him to live with him in the same house, despite the mother and the girl's parents agreeing?

You must obey your parents unless they command disobedience or the forfeiture of a right. Your wife has the right to an independent dwelling, and your father's objection to this is a forfeiture of this right. Therefore, there is no impediment to your marriage outside your father's house. However, if your father objects to a specific girl, then obedience to him is obligatory, because his obedience is obligatory, whereas marrying a specific girl is not obligatory. The best approach is to reconcile obedience to him with achieving your goal by gently persuading him, making supplications, and involving righteous people as intermediaries.