How can the father be persuaded to allow me to use his car, despite his vow which the questioner believes to be void and harmful, knowing that he needs it for commuting to work and that the car is rarely used?

If the son did not intend the financial assistance to his father as a donation or a gift, then he has a right to the thing he helped with. However, since the questioner intended what he previously paid for the first car as charity, he has no share in it.

As for the father's vow not to give the questioner the car, it is a "vow of obstinacy and anger," for which the vow-maker has the choice between fulfilling it or paying an expiation for an oath.

Therefore, the questioner is advised to convince his father of his need for the car, and to reassure him that he will take care of it. He may also seek help from relatives who hold a position of respect with his father. Furthermore, it can be explained that it is permissible for the father to retract his vow by paying an expiation for an oath.