Is it permissible for the son's wife to perform Hajj on behalf of her husband's father, who is unable to perform Hajj, given the disagreement among the siblings over who is more entitled to the Hajj spot?

If the father is unable to travel for Hajj due to an incurable illness while still retaining his sanity, the preponderant opinion is that it is obligatory for someone to perform Hajj on his behalf from his homeland. However, if he has lost his mental faculties and this loss is expected to be temporary, then it is not permissible for someone to perform Hajj on his behalf until he recovers. But if his loss of mental faculties is not expected to be temporary, then it is permissible for someone to perform Hajj on his behalf without his permission, by analogy with the deceased. If the father has already performed the obligatory Hajj, or if he has not performed Hajj and does not have the financial means, then it is not obligatory for someone to perform Hajj on his behalf, and an attempt should be made to reclaim any paid amount if possible. If the children disagree on who should take his place in approving the Hajj, lots should be drawn among them, and whoever wins the draw should pay the money to his father and take his place.