All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
The respected questioner did not clarify to us what he meant by the term "at the time of Nikah" and he did not clarify to us the wording used in authorizing his wife to divorce him. Anyway, in general, we say that in principle divorce is in the hands of the husband, the bond of marriage is in his hands and it is only him who can divorce, and a woman cannot divorce herself unless the husband authorized her to this effect.
If, by the expression 'at the time of Nikah', you meant that your wife conditioned this in the marriage contract, then this condition is void according to the view of the majority of the jurists as this is contrary to the objectives of a marriage contract and there is no consideration for her divorcing herself.
Nonetheless, if the husband says at the time of the marriage contract "I marry you but the matter (of divorce) is in your hands", then the marriage contract is correct but the matter is not in her hands because the authorization took place before the marriage contract.
However, if he authorizes her to divorce after the marriage contract, then the majority of the jurists are of the view that it is valid but they restricted it to the meeting in which the woman was informed about the authorization. Thus it is not valid for her to divorce herself after that meeting. They also stated that if the husband has intercourse with his wife, then the authorization becomes void. Ibn Qudaamah said: 'If her husband has intercourse with her, it means that he has cancelled his authorization. Giving her the attorneyship to divorce herself is a kind of authorization and if one acts on something upon which he has given authorization to others, then his authorization becomes void.'
Moreover, the authorization also becomes void if the husband invalidates it. So, if the husband in question had intercourse with his wife after he had authorized her regarding divorce, then the authorization becomes void and there is no consideration for her divorcing herself even according to the opinion of the scholars who are of the view that the authorization is not restricted to the meeting in which it was said, as is the opinion of the Hanbali School of jurisprudence.
Therefore, even if the wife has uttered the word divorce, she is still considered your wife and this does not affect the marriage contract.