Does the wife's failure to adhere to the conditions "By God, if you don't shut up, this will be the last word I have with you," with the husband's intention that the silence be temporary, constitute a breaking of an oath?

If you swore to your wife that if she did not stop talking, that would be your last word with her, and she did not stop, then you have two options: First: To fulfill your oath, and nothing is required of you. Second: To break your oath, and an expiation for the oath becomes binding upon you. This latter option may be more preferable, due to the saying of the Messenger of Allah, peace and blessings be upon him: "Whoever swears an oath, then sees something better than it, let him do that which is better, and make expiation for his oath." One should be careful of marital problems, and respect and understanding should prevail. Part of a woman's honoring her husband is her respect for his mother and avoiding ill-suspicion.