Is the husband obligated to provide for his wife's mother, who has no one to support her except her daughter and her daughter's husband, and is it permissible to give her zakat if providing for her is not obligatory?

A husband is not obligated to provide for his wife's mother, even if she is poor. However, it is commendable for him to treat her kindly, and it is permissible for him to give her from his zakat if she is eligible to receive it.