My sister-in-law embraced Islam but her mother is still a Christian. Is it permissible for her to uncover her head in front of her mother?

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.

First of all, we congratulate this sister for embracing Islam and we ask Allaah Almighty to keep her steadfast.

As for uncovering her head in front of her mother, this is permissible according to the opinion of some scholars. Moreover, some scholars are of the opinion that a Muslim woman is permitted to uncover all her body parts in front of a non-Muslim woman, with the exception of what is between the navel and the knees. This is the soundest of the Hanbali scholars' opinions. 

Allaah Knows best.