Is the action of my relative, whom God has enriched and who is an ascetic, not using his money for worldly pleasures correct, or should I advise him to do so, knowing that some of his children desire to enjoy permissible things and are sometimes deprived of them?

If your relative does that out of humility and asceticism concerning worldly matters, and out of devotion to the Afterlife, not out of concealing Allah's bounty or out of stinginess, while sometimes being generous to his family and spending his money on good deeds, then this is a praiseworthy act.