What should I do about the girl's family refusing to marry her to me, despite my desire to correct my mistake by marrying her after an illicit relationship occurred between us?

The relationship of love between young men and women is forbidden in Islam. Whoever has committed zina (fornication/adultery) must perform sincere repentance to Allah by cutting off the relationship with the girl, regretting the sin, resolving never to return to it, concealing his sin and hers, and hastening to marry a chaste Muslim woman of good religious character.