Is it permissible for a daughter to give zakat from her sick mother's money without her knowledge, and is she required to return what she gave to the heirs after the mother's death?

The daughter's action is incorrect because the zakat on the wealth of adults requires intention or authorization from its owners. She must return the money she took out to the heirs, and then demand that they pay the zakat if the deceased did not pay it and left an estate. And Allah knows best.