Must I divorce my wife, with whom I constantly disagree and who wishes for divorce due to our incompatibility and differing temperaments, knowing that she has a daughter from me and is my maternal cousin's daughter?

Divorce is not a trivial matter, and should only be resorted to when all means of reconciliation have been exhausted. If the spouses can live together and associate with kindness, that is preferable to separation. Keep your wife and do not divorce her, and live with her kindly, and explain to her that seeking divorce without a valid reason is forbidden. Deal with her wisely, and know that achieving affection and understanding requires patience, overlooking mistakes, and focusing on the good aspects. Be keen to adhere to the Sharia and cooperate with your wife in obedience to Allah. Know that among the reasons for the happiness of spouses are for the husband to treat his wife well, for the wife to obey her husband in what is right, and for both spouses to strive for contentment.