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.
The presence (and consent) of the guardian is a condition for the validity of the marriage contract whether the woman is a Muslim or from the People of the Book, as the Prophet said: "A woman cannot get married except with the permission of her guardian." [Abu Daawood]
Therefore, if this woman is from the People of the Book, then her guardian should be one of her relatives, who is of her religion, because a Muslim cannot be a guardian for her. However, if she has no guardian from the same religion like her, then the Muslim judge, or someone who could act on his behalf, would act as her guardian. So if the Imaam acted as her guardian despite the existence of her non-Muslim guardian, then this marriage is void according to the most predominant opinion of the scholars. In which case, she is not considered as your wife and it is forbidden for you to have sexual intercourse with her. However, we hope that you are not sinful -Allaah willing -for the sexual relations you had with her since you believed that this marriage was valid. However, you are obliged to invalidate this marriage contract by divorcing her in order to be on the safe side, since some scholars consider marriage without the presence or approval of the guardian as correct.
Nonetheless, if the Imaam acted as her guardian because she had no non-Muslim guardian, then the marriage is correct, since the Imaam acts on behalf of the Muslim judge in that country.
Besides, if this woman is (as you mentioned) insisting on her disbelief and you fear to have children with her, if Allaah blesses you with any children, and fear other religious disadvantages, then we believe it is best to divorce her before it is too late.
Finally, it should be mentioned that a Muslim man should marry a pious Muslim woman who would help him in his religious matters and in bringing up his children on a correct creed and good morals.
Allaah Knows best.