Does divorce occur with the statement: "It is forbidden for me if you speak with my brother's wife that you go to your parents' house," if the wife speaks with her brother-in-law's wife with the husband's permission after the oath, and is expiation (kaffarah) obligatory if divorce does not occur?

Since you intended by your oath to prevent your wife from speaking to your brother's wife without your permission, and not absolutely; you have not broken your oath by her speaking to her with your permission, and no divorce occurs, nor are you required to pay expiation. This is because intention in an oath specifies the general and restricts the absolute. You should be cautious of swearing by 'haram' or by divorce in the future, as the permissible oath is by Allah Almighty.