How can a compromise be reached between the daughter's desire to marry her former fiancé, who is also her maternal cousin, and her mother's absolute refusal of this marriage, given that her father approves?

Your duty is to please your Lord by severing your relationship with your cousin (son of your maternal aunt) because he is a non-mahram. He should propose to your father for marriage. Your mother has no right to prevent him from marrying you, and her consent is not a condition for the validity of the marriage. If he is suitable for you and you desire to marry him, your father has no right to prevent you, otherwise he would be considered an 'adil (one who prevents a woman from marrying a suitable suitor). It is preferable to appease your mother and try to persuade her to agree, and you must honor your mother and be good to her.