Is it permissible for a husband to designate the use of his car exclusively for his first wife, while denying its use to his second wife, knowing that he is well-off and able to be just between them regarding overnight stays and needs? And is it permissible for him to buy a private car for the second wife?

A husband must be equitable between his wives in terms of maintenance, clothing, and housing, providing each with what is customarily due to her. If he fulfills this, there is no harm in him singling out one of them for something extra in terms of maintenance or vehicles, because perfect equality in all these matters is difficult to achieve. Therefore, there is no harm if the husband allows his first wife to use his car, provided he gives the second wife what is due to her. It is also permissible for him to buy a car and allow the second wife to use it, as this is an act of honoring the wife and treating her kindly.