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.
A Muslim is allowed to share cooking utensils and food utensils and the like with non-Muslims, whether they are relatives or not. It is proven that the Prophet, sallallaahu ‘alayhi wa sallam, performed ablution from a water skin that belonged to a polytheist woman. An exception to this is applicable if a Muslim knows or predominantly thinks that the non-Muslim uses these utensils to serve an impure food such as pork, or drink such as alcohol and the like; in that case he should not use them.
In any case, a Muslim is advised to diligently invite his non-Muslim relative to Islam; perhaps Allaah will make him a reason behind his relative embracing Islam. The Prophet, sallallaahu ‘alayhi wa sallam, was reported to have said, “If Allaah guides one single man through you, that would be better for you than possessing the red camels [i.e. better than massive wealth].” [Al-Bukhari and Muslim]
Allah Knows best.