All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
It is invalid that a non-Muslim man acts as a Muslim woman’s Wali (guardian) in her marriage contract, and there is no difference of opinion among the scholars in this regard. Ibn Qudaamah said in Al-Mughni: “As for the non-Muslim, according to the scholarly consensus of opinion, including Maalik, Ash-Shaafi‘i, Abu ‘Ubayd, and the Hanafi scholars, it is not valid for him to act as a Muslim woman’s Wali under any circumstances. Ibn Al-Munthir said: ‘There is consensus on this point among all the scholars on whose authority we report.’” [End of quote]
Accordingly, the marriage contract in which your wife’s non-Muslim father acted as her Wali is invalid. If you wish to retain your relationship with this woman, then you must renew the marriage contract with her Muslim Wali in the presence of two witnesses. If her father is still non-Muslim and she has a Muslim guardian such as a grandfather, brother, nephew, paternal uncle, or paternal cousin, he may act as her Wali in the marriage contract. If she has no Muslim male relative to act as her Wali, the Muslim judge may act as her Wali in the marriage contract, and if not, then the head of the Islamic center in her country of residence should act as her Wali. If this option is not available either, then any trustworthy Muslim man may act as her Wali with her permission.
For more benefit on the sequence of woman's guardians in marriage, please refer to Fatwa 83338.
Also, for more benefit that a non-Muslim man cannot be a Wali (guardian) of a Muslim woman in marriage contract, please, refer to Fataawa 225424, 88488, 86524, and 246439.
Allah Knows best.