For families all over the world, going through a pandemic has presented a number of challenges. In particular, social distancing measures involving the closure of schools and day care centers, as well as increasing work hours at home, made parents face very demanding situations. However, we know little about whether parents’ burnout levels are influenced by the age of their children. This study sought to determine whether levels of parental burnout (PB) are higher in families with at least one child under the age of four than in families with older children (5 to 18 years). The second goal was to explore whether having children under 4 years of age moderates the relationship between parental cooperation and PB. A cross-sectional study was conducted with a sample of 651 participants (525 mothers and 126 fathers) since May 18th until August 27th, 2020. The main results showed that child age is a predictor of PB. Besides, having a child aged 0–4 years old moderates the relationship between parental cooperation and PB. Finally, it was found that in cases where there was at least one child under 4 years of age in the family, with one of the partners who worked remotely, the respondent’s PB rose by 7.9 points. The implications of these results with respect to the consideration of children’s ages in the different parental scenarios were discussed.