All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
What the daughter did was wrong since an intention is vital in paying the zakat of an adult Muslim or at least one should have the authorization of the owner. Hence, she should pay the money that she paid of zakat from her mother's money back to the heirs and then ask them to pay the due zakat on their money if the mother had not already paid it on this money. The heirs should first pay the zakat before dividing any of the inheritance.
Allaah Knows best.