In response to this question, Dr. Monzer Kahf, a prominent economist and counselor states:
1. Your husband’s Zakah may be given to any of your family members (of course except you because your expenses are your husband’s responsibility) provided they are poor that they deserve Zakah. Being under debts that one can’t pay them from one’s own resources is a part of being poor. In this specific case you need to really be careful that your mom and other family members are really in need for this help (for instance, did your father leave any property that put the rest of the family outside poverty?). If you give Zakah you may give as much as needed to pay the debts or to relieve the recipient from the hardship that Zakah is given for. In this case for instance you may give for payment of all the debts.
2. I don’t consider payment for education as important as payment to relieve people from hunger. Hence, where ever you are from there is a great deal of hunger in our Muslim countries and in non-Muslim countries that makes education a kind of luxury under these circumstances. Please do not give Zakah for education leave it for stomachs and other pressing necessities at this time.
If the pension of your mom allows her and her child to live modestly, they are not eligible for Zakah (it is then only for debt payments) especially that we live in a time when there are about thirty five thousand Muslim children who die every day out of hunger.”