Is it permissible for my mother to slaughter the vowed sheep at home instead of in the middle of the neighborhood, then distribute it to the poor of the neighborhood, if the number of poor people is large and it is not possible to distribute it to everyone in the middle of the neighborhood?

Whoever vows obedience must fulfill it. If they specify a place or time for it, they must fulfill it as specified. If they fail to do so, they must, in addition to fulfilling the vow, offer an expiation for an oath (kaffarat yameen). If it is impossible to fulfill the vow in its specified place or time, then it must be fulfilled along with an expiation for an oath. The original intention is for the mother to slaughter the animal in the middle of the neighborhood as she vowed. If she does not do so, then in addition to the animal, she must offer an expiation for an oath: feeding or clothing ten poor people. If she cannot find them, then fasting for three days.