Is it permissible to take back one's wife after having issued a single oath of divorce to her, knowing that this occurred after an argument between the spouses, and the husband asked the wife's father not to let him utter it, but the wife insisted?

Your question is unclear. If you uttered the divorce (talaq) while being aware of what you were saying, then it has taken effect. You may reconcile with your wife (raj'ah) before the expiration of her waiting period (iddah), provided you have not divorced her more than once before. Reconciliation occurs through speech or sexual intercourse.