Is the husband considered an oppressor or is he in the right for divorcing his wife who annoys him and bargains with him, despite his providing housing and expenses for their daughter, and the wife's claim against him that he will be punished and that she has repented, while he is unable to forget her past?

Repentance from illicit relationships is obligatory. This woman wronged herself by engaging in this relationship willingly and voluntarily. Divorce is permissible and disliked unless there is a need for it. You are not wronging her merely by divorcing her, and you are not obligated to take her back. If it is possible to take her back, then do so, especially if she has repented and you have a daughter with her, for family stability aids in good upbringing. If you desire to take her back and she is still in her 'iddah (definition) (waiting period), you may take her back without a new marriage contract. However, if she has become irrevocably divorced from you, a new contract is necessary, with the permission of her guardian and the presence of witnesses.