Is it permissible for the supervisor of the will's execution to delegate another family member to take her place in supervising with the executors, especially since she is about to travel?

The jurists differentiated between the Mutawalli (administrator) of an endowment (waqf) and the Nazir (supervisor). The Mutawalli disposes of its funds, while the Nazir is responsible for its preservation, its revenues, and the implementation of its conditions. If the endower (waqif) specifies both a Mutawalli and a Nazir, then the Nazir acts as an overseer. The Nazir is not permitted to delegate the supervision to another, unless the endower has allowed him to do so. The Nazir may appoint someone to act on his behalf in the transactions that he is authorized to perform.