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, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
It is impermissible for the father to prevent his daughter from remarrying her ex-husband. Allaah The Exalted Says (what means): {And when you divorce women and they have fulfilled their term, do not prevent them from remarrying their [former] husbands if they agree among themselves on an acceptable basis.} [Quran 2:232]
Hence, the divorced couple may remarry with a new marriage contract and a new dowry; for Khul' is considered an irrevocable divorce. Therefore, the father should comply with the Command of Allaah The Exalted and not prevent his daughter from remarrying her ex-husband. It was reported in Saheeh Al-Bukhari that the sister of Ma‘qil ibn Yasaar was divorced by her husband who left her until she had fulfilled her term of ‘Iddah (post-marriage waiting period which should elapse before she can remarry), and then he wanted to remarry her but Ma‘qil refused. Hence, this verse was revealed; Allaah The Exalted Says (what means): {… do not prevent them from remarrying their [former] husbands if they agree among themselves on an acceptable basis.} [Quran 2:232]
The Prophet, sallallaahu ‘alayhi wa sallam, sent for Ma‘qil and recited the verse to him and consequently Ma‘qil gave up his zealous spirit, yielding to the Command of Allaah The Exalted; as his sister wanted to go back to her ex-husband.
However, it is impermissible for the questioner to remarry her ex-husband without the consent of her Wali i.e. legal guardian, her father in this case. She should try persuading her father to approve of their marriage and to not prevent her from remarrying her ex-husband, highlighting that such act is prohibited. She should show him this Fatwa, and if he insists on his refusal and on preventing her from remarrying her ex-husband, then she is entitled to take her case to the concerned Islamic court so that the judge would marry her off or authorize another person to do so.
Allaah Knows best.