Is it permissible for a woman to stipulate to her husband that he relinquish his legitimate rights after he marries another?

Your duty is to treat your husband with kindness and fairness. It is not permissible for you to withhold his right to intimacy because he married another woman. If you do so, you expose yourself to severe warning. Abu Hurayrah (may Allah be pleased with him) narrated that the Prophet (peace and blessings be upon him) said: "If a man calls his wife to his bed, and she refuses to come, the angels curse her until the morning." (Agreed upon). You do not have the right to stipulate anything you mentioned in exchange for obeying him. However, you may waive some or all of your right to fair division of time, if he agrees to that.