All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
It is not clear to us what you mean by going separate with your wife. If you mean divorcing her, then that is allowed, but it is disliked if there is no need for it. If your parents command you to divorce your wife, you are not obliged to obey them in this regard if they do not have a valid reason; please refer to fatwas 84808 and 253468.
However, if you mean that you wish to live with your wife in a separate house, then you have the right to do so even if your parents do not agree. Your wife is entitled to a separate accommodation where she would be at ease without inconvenience or hardship, as has been stated by the scholars and as we have previously underlined in fatwa 84608.
Also, you are not obliged to obey your parents in marrying another wife. The obedience to parents is not obligatory in all matters and under all circumstances; rather, it is restricted to what is beneficial for them and does not harm their child. Please, refer to fatwa 131695.
We advise you to be patient with your parents and to ask Allah, The Exalted, to guide them to the truth. Try to use wisdom to appease them as much as you can so that you avoid making them angry and at the same time preserve your marriage and the stability of your family.
We ask Allah to give you support and make your efforts successful.
Allah knows best.