Our Sages relate that Abba Chilkiya and his wife [Shelmrus] both gave tzedakah. When there was a lack of rain, they both davened for rain, but her prayers were accepted before her husband’s.
Our Sages explain that Abba Chilkiya’s tzedakah was in the form of money, and then with that tzedakah money, the poor needed to buy the food to satiate their hunger, while his wife would give the actual food to the poor.
In another source, our Sages say, עושה צדקה בכל עת זה הזן בניו ובנותיו כשהם קטנים (“‘One who performs charity at all times’: This refers to one who supports his sons and daughters in their infancy”). This means that the concept of tzedakah applies not only to strangers, but also to one’s own children. This refers not only to material tzedakah, for spiritual tzedakah, which includes the chinuch of one’s children, is also considered tzedakah.
Just as regarding material tzedakah, the husband gives the poor person the means of obtaining food, while the wife gives the food itself, so too is it regarding spiritual tzedakah, the chinuch of children. The husband, the father, gives the children the means to obtain a chinuch, while the mother gives the spiritual food itself. For although the father has a mitzvah of ושננתם לבניך (“And you shall teach them to your children”), in most cases it is not the father himself who teaches his children; rather, he hires a teacher for them.
It is told that one day the Alter Rebbe called one of his chassidim and said to him, “I have the obligation of ושננתם לבניך, (“And you shall teach them to your children”), and you have the mitzvah to provide parnassah for your household members. Let’s trade: I will provide the parnassah for your household members, and you teach my son Berel (The Miteler Rebbe).”
Hence, the father does not give the spiritual sustenance itself; the teacher does this through the money that the father gives to him.
It is not so with the mother: The mother gives her children the spiritual sustenance itself. She teaches the child to wear a tallis katan, to wash negel vasser, to recite brachos, and so on. Afterwards as well, when the child grows and learns in Talmud Torah or yeshivah, he can, during the time he is home, lose or fail to retain what he receives from these institutions. The mother must then be careful to direct him toward proper conduct.
(Likkutei Sichos, vol. 2, p. 580 ff.)