Is it permissible for a wife to sell a piece of clothing she bought for 7.5 pounds to her aunt's daughter for 15 pounds, claiming that this is a form of trade after purchasing it with her own money?

It is impermissible for an agent to purchase for himself from his principal, just as it is impermissible to purchase from himself for his principal, especially if it is customary to purchase from another, due to the suspicion involved. Therefore, the questioner's wife must return the excess amount to her maternal aunt's daughter.