What is the ruling regarding my continued residence in the marital home with my husband after he pronounced the oath of divorce upon me, while he refuses to reconcile and insists on the divorce? And does the sin fall upon both of us or upon him alone if continued residence is unlawful?

If this was the first divorce and it was not for a financial consideration, then it is a revocable divorce, and the husband has the right to take his wife back during her waiting period (iddah). The wife must remain in her husband's house and is not permitted to leave it, nor is the husband permitted to expel her from it until her waiting period (iddah) ends, in accordance with the Almighty's saying: "Do not expel them from their homes, nor should they leave, unless they commit a clear immorality." It is permissible for the husband to be alone with his wife, and for her to adorn herself for him, as long as she is within the iddah of a revocable divorce.