Is Zakat obligatory upon receiving money inherited from our father who passed away and may have already paid Zakat on it, and is it permissible to give Zakat to his two poor, married daughters?

Your father's financial liability is originally clear, so you are not obligated to pay zakat on his behalf if its obligation is doubtful. If the heir's share of this wealth reaches the nisab and a full year passes, zakat becomes obligatory on it. It is permissible to give zakat to poor sisters, for the Prophet, peace and blessings be upon him, said: "Charity given to the poor is charity, and charity given to a relative is two: charity and upholding ties of kinship."