Praise be to Allaah.
The husband of your mother-in-law (your husband's mother), who is not your husband's father, is not one of your mahrams, because there is no reason of ties through blood, marriage or breastfeeding to make him a mahram. Allah, may He be exalted, says (interpretation of the meaning):
Forbidden to you (for marriage) are: your mothers, your daughters, your sisters, your father's sisters, your mother's sisters, your brother's daughters, your sister's daughters, your foster mother who gave you suck, your foster milk suckling sisters, your wives' mothers, your step daughters under your guardianship, born of your wives to whom you have gone in - but there is no sin on you if you have not gone in them (to marry their daughters), - the wives of your sons who (spring) from your own loins, and two sisters in wedlock at the same time, except for what has already passed; verily, AllÃ¢h is OftÂ¬Forgiving, Most Merciful.
Also (forbidden are) women already married, except those (slaves) whom your right hands possess. Thus has AllÃ¢h ordained for you. All others are lawful
[al-Nisa' 4:23, 24].
Allah has explained to His slaves the women who are forbidden in marriage. They include: the wife of a man's son who is his own offspring and not an adopted son, as was the case during the Jaahiliyyah, and not as mentioned in your question. Your husband is not a son to his mother's husband. The man mentioned here is a stranger to you and is not one of your mahrams, so it is not permissible for you to take off niqaab in front of him.
This is also explained in another verse which describes to a woman her mahrams in front of whom she may take off her khimaar (head cover) or show any of her adornments. Allah, may He be exalted, says (interpretation of the meaning):
And tell the believing women to lower their gaze (from looking at forbidden things), and protect their private parts (from illegal sexual acts) and not to show off their adornment except only that which is apparent (like both eyes for necessity to see the way or outer dress like veil, gloves, head-cover, apron, etc.), and to draw their veils all over Juyubihinna (i.e. their bodies, faces, necks and bosoms,) and not to reveal their adornment except to their husbands, or their fathers, or their husband's fathers, or their sons, or their husband's sons, or their brothers or their brother's sons, or their sister's sons, or their (Muslim) women (i.e. their sisters in IslÃ¢m), or the (female) slaves whom their right hands possess, or old male servants who lack vigour, or small children who have no sense of the feminine sex. And let them not stamp their feet so as to reveal what they hide of their adornment. And all of you beg AllÃ¢h to forgive you all, O believers, that you may be successful
The scholars of the Standing Committee were asked:
Is it permissible for a woman who is married to a man to show her face in front of his mother's husband and his brother through his mother?
They replied: It is not permissible for a woman to show her face in front of her husband's mother's husband or to his brother through his mother, because they come under the general meaning of those from whom she is obliged to observe Hijab. End quote.
And Allah knows best.
For more information, please see the answer to question no. 5538 and 120041.