Can a woman marry a man with whom she repented after committing adultery and gave birth to a child, with only her father's consent, knowing that her mother rejects this marriage?

If you both sincerely repent from the indecency you committed, then there is no impediment to your marriage. Your disagreement with your mother on this matter is not considered disobedience. However, you must still be dutiful and kind to her. Know that the majority of jurists hold the view that a child born out of wedlock is not attributed to the lineage of the fornicator.