Does a wife become forbidden to her husband if he tells her: "Do not leave the house except with my permission, and if you leave the house, you are forbidden to me just as my mother is forbidden to me," and then she leaves without his permission?

This statement is a conditional ẓihār, contingent on the wife leaving the house without the husband's permission. Since she did leave without his permission, the ẓihār has taken effect. It is not permissible for him to have intercourse with her before he performs the expiation for ẓihār. He must also repent to Allah for this forbidden statement.