It is critically important to understand the environmental contexts and demographic factors that put families at greater risk of COVID-related parenting stress. The current study examined a new scale measuring situational stress caused by concern about family safety and stability during the COVID-19 pandemic. We examined how this stress differed by socioeconomic status and children's schooling modality, and how this stress and parent social support affected parents' severity of overall psychological distress. Parents of children in distance learning experienced significantly less COVID-related family safety/stability stress. COVID-related family safety/stability stress was a significant predictor for severity of psychological distress, and this positive relationship was significantly moderated by perceived parent social support, controlling for all other predictors. Going forward, financial resources and perceived parent social support should be incorporated in plans to assist parents during the pandemic, as these serve as protective factors from COVID-related family safety/stability stress.