Is it permissible for a mother to distribute the saved money, which a hawl (full lunar year) has passed over, among her daughters only, and is zakat obligatory on it after its distribution, if that is permissible?

If a mother divides her money among her children before a full year has passed, she is not obligated to pay zakat on it. Zakat becomes obligatory only upon the one who possesses it, if it reaches the nisab (minimum threshold) and a full year has passed since the time of possession. If she divides it after the year has passed, then she is obligated to pay its zakat.