Is it permissible for my wife to perform Hajj on behalf of her deceased father, given that she made another vow and fears that it might be an overstepping of bounds with God?

A vow contingent on a disliked condition is, according to the preponderant opinion, reprehensible, but it must be fulfilled. Therefore, the woman must perform Hajj on behalf of her father if the condition is met. However, if the vow is not contingent, there is no reprehensibility in it, and its fulfillment is obligatory as a matter of course.