A woman uncovering her face in front of a Muslim or a non-Muslim woman
Is it permissible for a Muslim woman to show her face in front of a non-Muslim woman?
Is it also permissible for her to uncover her face in front of her mother-in-law who is a non-Muslim?
There is no harm in a woman uncovering her face in front of any woman whether a Muslim or a non-Muslim. This is because she was only asked to cover her face in front of men who are non-Mahrams (not a spouse or an unmarriageable relative). Allah (Exalted be He) says:
...and to draw their veils all over Juyûbihinna (i.e. their bodies, faces, necks and bosoms) and not to reveal their adornment
until His Saying: (Part No. 17; Page No. 288)
...or the (female) slaves
Allah (Exalted be He) orders women to cover their face and chest with the Khimar (veil covering to the waist) in the presence of men except for her Mahrams (spouse or unmarriageable relative) who are mentioned in the Ayah (verse of the Qur'an) or those who are made forbidden for her in marriage because of suckling as it has been mentioned in other evidence. The word "women" mentioned in the Ayah includes all women; whether Muslims or non-Muslims. And Allah knows best. May Allah grant us success. May peace and blessings be upon our Prophet Muhammad, his family, and Companions.