The coronavirus pandemic poses a substantial threat to people across the globe. In the first half of 2020, governments limited the spread of virus by imposing diverse regulations. These regulations had a particular impact on families as parents had to manage their occupational situation and childcare in parallel. Here, we examine a variation in parents' and children's stress during the lockdowns in the first half of 2020 and detect the correlates of families' stress. Between April and June 2020, we conducted an explorative online survey among n = 422 parents of 3- to 10-year-old children residing in 17 countries. Most participants came from Germany (n = 274), Iran (n = 70), UK (n = 23), and USA (n = 23). Parents estimated their own stress, the stress of their own children, and various information on potential correlates (e.g., accommodation, family constellation, education, community size, playtime for children, contact with peers, media consumption, and physical activity). Parents also stated personal values regarding openness to change, self-transcendence, self-enhancement, and conservation. The results indicate a substantial variation in the stress levels of families and their diverse reactions to regulations. Media consumption by children commonly increased in comparison to the time before the pandemic. Parents raising both pre-school- and school-aged children were at a particular risk of experiencing stress in response to regulations. Estimated stress and reactions varied with the age of children and the personal values of parents, suggesting that such variables need to be considered when implementing and evaluating regulations and supporting young families in the current and future pandemic.