Is it permissible to supplicate for one's own death for the guidance of relatives who do not pray in congregation and listen to objectionable things, believing that the supplicator's death will be the cause of their guidance because they are young and do not take death into account?

It is not legislated to wish for death for the guidance of creation, for the Prophet, peace and blessings be upon him, and his companions did not wish for death for that purpose. What is legislated is to wish for a long life in obedience to Allah. A Muslim should strive to invite to Allah with wisdom and good admonition, and reminding people of death and providing real-world examples of it are sufficient to soften hearts without wishing for death, which is forbidden.