Is the wife's cousin considered her brother through rada'a (nursing) if the wife was nursed by her aunt (the cousin's mother)?

Nursing (Radha'ah) only affects the nursed child (radhi') and his offspring. As for his ascendants and collaterals, they are not affected. Therefore, the brother of your wife's sister through nursing is not your wife's brother, because nursing does not affect the collaterals of the nursed child.

Sheikh Muhammad bin Uthaymeen said: "Nursing relates to the nursing mother and her ascendants, descendants, and collaterals, and it relates to the owner of the milk (the father) and his ascendants, descendants, and collaterals. As for the nursed child, nursing relates only to him and his descendants. Nursing does not affect his ascendants or collaterals. Thus, it is permissible for the brother of the nursed child to marry the woman who nursed his brother, and it is permissible for the father of the nursed child to marry the woman who nursed his son. However, it is not permissible for the son of the nursed child to marry the nursed child's sister from the woman who nursed him."