Is it permissible for a mother not to wear a hijab in front of her daughter's husband, and what is the evidence for that?

The mother of the wife becomes forbidden to her daughter's husband simply by virtue of a valid marriage contract. She is one of his eternally forbidden (mahram) relatives, as stated in the Almighty's words: "and your wives' mothers." Therefore, the wife's mother is not obligated to wear the hijab in front of her daughter's husband, and he is permitted to see from her what a man may see from his mahram relatives.