Is it permissible for the children to appoint their maternal uncle to perform Hajj on behalf of their deceased father, given that they are capable of performing Hajj themselves, and knowing that the uncle has performed Hajj previously while they have not yet?

It is better for one of the children to perform Hajj on behalf of their deceased or incapacitated father than to appoint a stranger, because their devotion to their father is greater. It is recommended for a child to perform Hajj on behalf of their deceased or incapacitated parents. However, it is not obligatory for the children to perform Hajj themselves; rather, it is permissible for them to appoint a stranger, such as their maternal uncle, to perform Hajj on behalf of their father, especially if there is another benefit in that, such as him being a mahram to their mother.