The present study seeks to contribute to developmental science in emergencies by investigating associations between COVID-19 pandemic-related stressors, parents’ stress, family relationships, and child wellbeing. In doing so, we build on recent research that generalizes the assumptions of the Family Stress Model beyond direct economic stressors of households to macro-contextual stressors that operate at the societal level. In the case of our study, these stressors relate to the COVID-19 pandemic, such as health risks and confinement-related stresses. Participants were 783 parents of young children (75% female, Mage = 34.61 years) residing in the United Arab Emirates. They completed an online survey in Fall 2020 and Spring 2021, measuring how the pandemic impacted their lives and the lives of their child (Mage = 47.54 months). A subsample of parents (n = 96) completed the survey for two children. Structural equation modeling showed that pandemic-related stressors contributed to higher stress among parents which, in turn, resulted in lower parent-reported child wellbeing at various times during the pandemic. Family relationships mediated the association between parents’ stress and child wellbeing. The present study contributes to our understanding on how large-scale disruption due to COVID-19 pandemic-related stressors gets inside the family, the strength and direction of associations (concurrently and over time), and the timing of mechanisms that impact family processes. The results highlight the need to support families with young children in managing disruptions due to emergencies, such as a global public health crisis, and to determine ways of preventing longstanding consequences on family structures and children’s lives.