Stress management in organizations has traditionally been an important issue, and managing stress in organizations is of paramount importance in contemporary work settings characterized by rapid-paced and high-demand environments (Abbas & Raja, 2019). The extensive scholarly inquiry has focused on investigating the association between stressors, particularly with regard to challenge and hindrance stressors, and organizational outcomes within the domains of organizational behavior, social science, and management. Nevertheless, the existing body of research has yielded inconsistent findings when it comes to the impact of challenge and hindrance stressors on organizational outcomes (Haldorai et al., 2022; Kubicek et al., 2022; LePine et al., 2016; Liu & Li, 2018; Podsakoff et al., 2023). Within this context, the primary aim of this study is to explore the potential roles of cognitive appraisals as a mediator in the influential dynamics of stressors, and family motivation, defined as the desire to make a meaningful contribution to one's family through work, as a moderator on the appraisal process, as well as on the subsequent reaction process. The theoretical foundations for this investigation draw upon transactional theory (Lazarus & Folkman, 1984) and the conservation of resources theory (Hobfoll, 1989). To conduct this empirical investigation, a three-wave online survey was employed, targeting a sample of 250 full-time employees. The selection of participants for this research was conducted from a variety of companies encompassing a wide array of industries, such as manufacturing, construction, banking and finance, and service sectors in Korea. The results of this study revealed that family motivation played a significant role in enhancing the positive association between challenge stressors and challenge appraisal. Similarly, family motivation intensified the strength of the relationship between hindrance stressors and hindrance appraisal. With respect to the reaction process, the examination of family motivation as a moderator demonstrated no significant impact on the connection between challenge appraisal and work effort. However, it exhibited mitigating effects on the negative associations between hindrance appraisal and work effort.