Grief and duty mix following a family member's death. Relatives nearest to the deceased are often assigned the roles of executors and trustees with time-sensitive duties to perform. Fiduciary responsibility begins the moment someone dies and continues until estate assets are distributed, as directed by the decedent or a court.
This question can only be answered by you as a testator, the will creator. The decision to designate a spouse or other relative as the executor of your estate depends on the qualities, abilities and willingness of the family member.