What should I do about my wife who frequently swears by Allah, sometimes falsely out of forgetfulness and not intentionally, and even though I have warned her, she continues to do so?

If a wife swears an oath believing she is truthful, and then it becomes clear that the opposite is true, there is no sin upon her and no expiation is required of her. This is not considered among the forbidden "false oaths" (al-yameen al-ghamūs), because error is forgiven, as stated in the Almighty's words: "And there is no blame upon you for that in which you have erred, but [only for] what your hearts intended." The wife should be cautious about being lenient in swearing frequent oaths, and the husband should advise her regarding this.