since the father is a strict sunni, it is assumed that he does not believe in the legitimacy of temporary marriage and therefore, will not grant permission.
the woman in this case has not been married before however is not a virgin due to having committed fornication before.
Islam has introduced temporary and permanent marriage as the legitimate ways of fulfilling one’s needs and desires. Temporary marriage refers to the marriage of a man and woman who have no barriers for doing so. It takes place with the consent of both sides of the contract and a specified dowry and timeframe. According to Islam, the validity of temporary marriage is contingent upon certain criteria being met[1], namely getting the father’s (and in the case of not having a father, the paternal grandfather’s) consent if the girl is a virgin. If the girl isn't a virgin and has lost her virginity through legitimate marriage, her father’s consent is no longer a condition, but if it has been lost as a result of shubhah intercourse (mistaken/confused/accidental intercourse) or illegitimate intercourse (adultery), it is a preferred precaution to get the father’s consent[2] (although it still isn't mandatory). Also, if a girl wants to get married (temporarily or permanently) and neither has a father nor a paternal grandfather, there will no longer be any need for permission from anyone else (regardless of whether she is a virgin or not).[3] Of course some mujtahids such as Ayatullah Nouri Hamedani say: “The father or paternal grandfather’s (in the case of not having a father) consent isn't a condition, although it is better for them not get married without having their opinion and permission. Nevertheless, the marriage of a virgin girl who hasn’t reached rushd (the stage in which one can distinguish between good and bad and can tell what is to his/her benefit) without the permission of her father is void.”[4] As for the marriage of Shia men with Sunni women, there are different viewpoints on the issue in fiqh; the famous verdict being that it is permissible,[5] especially when there are chances of the guidance of the woman to Shiism and the Ahlul-Bayt’s school of thought.[6] Nevertheless, since this girl’s virginity has been lost through other than marriage, she shares the ruling of virgins according to some mujtahids, and must get her father or paternal grandfather’s consent first.[7] For further information, you can refer to the following: 1- Marrying Sunni girls, Question 1254 (website: 1333). 2- Father’s consent regarding virgin daughter’s marriage, Question 4958 (website: 5248). [1] Question 1290 (website: 1275). [2] Tawdihul-Masa’ele Maraje’, vol. 2, pg. 459, issue 2377. [3] Tawdihul-Masa’ele Maraje’, vol. 2, pg. 387, issue 2376. [4] Question 1483 (website: 1530). [5] Naser Makarem Shirazi (kharej fiqh lessons on nikah [marriage], academic year 1381-1382 on his official website); Seyyid Sadiq Rohani, Fiqhul-Sadeq, vol. 21, pg. 469, from the software of this book from the institute of Al-Imam Al-Rohani. [6] With help from: Marrying Sunni girls, Question 1254 (website: 1333). [7] With help from: Marrying a Sunni girl, Question 2252 (website: 2376).