Recent evidence suggests that driving behavior and traffic safety outcomes of parents may be influenced by the extent to which they receive information and education on road safety, as well as the fact of driving with their children on board, which may increase their risk perception. However, there are no studies specifically addressing the case of crashes suffered while driving with children. Hence, this study aimed to describe the relationship between road safety education-related variables and parents’ traffic safety outcomes while driving with children on board. For this cross-sectional study, data was retrieved from a sample composed of 165 Spanish parents—all of them licensed drivers—with a mean age of 45.3 years. Through binary logistic regression (logit) analysis, it was found that factors such as gender, having received road safety education (RSE), and having been sanctioned for the performance of risky driving behavior contribute to modulating the likelihood of suffering crashes while driving with children on board. Gender differences showed a riskier status for male parents. In this study, a set of risk factors explaining the involvement in traffic crashes when driving with children as passengers was identified among parents: gender, traffic sanctions, valuation, and exposure to road safety campaigns. Also, substantial limitations in the self-reported degree of received RSE were found, especially considering that risky driving behavior and traffic crash rates with children on board still have a high prevalence among parents.