Is it permissible to deprive the wife of her legitimate rights (dowry, gold, and deferred dowry) if she requests divorce for harm due to her husband marrying another woman out of desire for procreation?

The Shari'ah did not stipulate a defect in the first wife as a condition for permitting polygyny. Rather, it stipulated the man's ability to marry and to be just between his wives. A man is not obliged to seek his wife's permission or inform her of his marriage to another. She is not entitled to seek divorce merely because he married another, as long as he fulfills her rights and acts justly between them, unless she stipulated in the marriage contract that he should not marry another. If she did not stipulate this, then she is not entitled to seek divorce, and the judge is not permitted to rule in her favor. If the wife cannot bear to remain with the husband after his second marriage, she may seek khul' (divorce at the wife's instance, usually with compensation to the husband) or divorce. The husband may refuse until she forfeits her right or part of her mahr (dowry) for him. If the husband agrees to divorce her without khul', then she is entitled to the mahr. If the gold was part of the mahr, then it is her right; otherwise, it is the husband's right. The husband is advised to practice polygyny if he is capable of being just. If the first wife requests a divorce, she should be advised, and the disadvantages of divorce should be explained to her. If she insists on divorce, she can be persuaded to drop the court case in exchange for part of the mahr.