What is the ruling on the conditions stipulated by the father after his death, and what is the ruling on the girl leaving without her husband’s permission after she refused to live with her husband’s mother?

The conditions stipulated by the wife in the marriage contract, including an independent dwelling, are valid and binding as long as they do not violate Islamic law. An independent dwelling is a right of the wife, whether she stipulates it or not. For the wife to leave the house without the husband's permission for a non-essential reason is an act of disobedience and forbidden insubordination (nushooz). The wife should fear Allah, obey her husband, and help him in being dutiful to his mother.