All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
The marriage of a man with a second wife is something that the wise Sharee'ah has permitted for whoever is able to be just between his two wives. So, there is nothing wrong with it Islamically, even if the people consider it as wrong based on their customs and traditions which contradict the Sharee'ah.
Indeed, you did well as you mentioned that you do not want to ask for a divorce. A wife is not permitted to ask for a divorce just because her husband has married another wife.
For more on the situations when a wife is permitted to ask for divorce, please refer to Fatwa 88408.
Also, your parents have no right to urge you to ask your husband to divorce you just because of the reason which you mentioned in the question, and you are not obliged to obey them in this regard. Indeed, obedience is required only in what is permissible and it is not permissible for the parents to ask their daughter to separate from her husband without a sound reason. Ibn Taymiyyah said, "If a woman is married, her husband has more dominance [right] over her than her parents, and she is more obliged to obey her husband than her parents."
Al-Mardaawi said, "She (the wife) is not obliged to obey her parents if they order her to separate from her husband."
Therefore, we advise you to have a good marital relationship with your husband and be gentle with your parents. You should try to convince them to change their mind and you should supplicate to Allaah to facilitate this for you. You may seek the help of some righteous people to influence your parents in this regard. Then, if they change their mind, all perfect praise be to Allaah, otherwise you should endeavor to attain their pleasure and you should not cut relations with them even if they cut relations with you, and you should be kind to them even if they mistreat you. This is because it is an obligation to fulfill their rights of kindness and obedience to them at all times.
Allaah Knows best.