Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Giving charity on behalf of a dead mother is permissible in Shariah and its reward reaches her for the Hadith reported by Ayisha (Radiya Allahu Anha) that a person came to the Prophet Muhammad (Sallallahu Alaihi wa Sallam) and said: Ayisha (Radiya Allahu Anha) that a person came to the Prophet (Sallallahu Alaihi wa Sallam) and said: ‘My mother died suddenly and I think that if she could speak, she would have given "charity." May I give charity on her behalf? He said, "Yes! Give charity on her behalf." [Reported by Imam al-Bukhari].
As for the Zakah obligatory upon you have to pay it yourself from your own belongings. You may give Zakah to those people to whom your mother used to give Sadaqah provided they are poor, needy, or those who are mentioned in the verse: {As-Sadaqât (here it means Zakât) are only for the Fuqarâ' (poor), and Al-Masâkin (the poor) and those employed to collect (the funds); and for to attract the hearts of those who have been inclined (towards Islâm); and to free the captives; and for those in debt; and for Allâh's Cause (i.e. for Mujâhidûn - those fighting in the holy wars), and for the wayfarer (a traveller who is cut off from everything); a duty imposed by Allâh. And Allâh is All-Knower, All-Wise.}[9:60]
Giving Zakah to the people to whom your mother used to give it with the intention of Sadaqah is not sufficient and it is not considered as Zakah.
Allah knows best.