Is it permissible to fulfill a vow made to other than Allah, such as a vow made to shrines, knowing that the mother fears the consequences of not fulfilling it?

It is not permissible to make a vow or offer a sacrifice to other than Allah Almighty, and this is major shirk (polytheism). Allah Almighty says: (Say, "Indeed, my prayer, my rites of sacrifice, my living and my dying are for Allah, Lord of the worlds. No partner has He.") The Prophet, peace and blessings be upon him, said: "Whoever vows to obey Allah, let him obey Him; and whoever vows to disobey Him, let him not disobey Him." Furthermore, erecting structures over graves is an innovation that can lead to shirk, and the Prophet, peace and blessings be upon him, forbade raising graves, building over them, plastering them, and taking them as mosques.