How can one deal with a husband who links the serenity of the marital relationship to the pleasure of his family, and who boycotts his wife's family because she refused to apologize to his cousin's daughter, whom his family considers like a sister to him, especially after he declared that she is "before me and before my children"?

If your husband's female cousin (daughter of his maternal aunt) is his mahram (definition) through breastfeeding, then she is his sister, and there should be no jealousy towards her unless there is a cause for suspicion. However, if she is a non-mahram (stranger) to him, he must lower his gaze, and it is not permissible for him to touch her. The wife has the right to feel jealous if the husband does something that provokes it, and she should advise him gently. The wife should avoid excessive jealousy, respect her husband's kinship with his maternal aunt's daughter, be patient with her husband's family, apologize if she offends, and try to draw closer to them to win the affection of her husband and his family. The wife has the right to an independent dwelling. We advise the husband to treat his wife kindly, be mindful of her feelings, and balance her rights with the rights of his family.