Background. The limitations imposed by governments for containing the spread of COVID-19 have affected familial relationships, especially those of families dealing with children with special needs or chronic illness conditions. The current study aims to better understand what pathological/disability condition has impacted parental resources, sense of competence, and perception of children’s executive functioning the most. Methods. A sample of 648 parents was asked to answer a survey assessing children’s condition (typical development, specific learning disorder, autism spectrum syndrome, chronic illness), parental resources, parenting sense of competence (distinguished into parental satisfaction and self-efficacy), and parents’ perception of their children’s executive functioning. A MANOVA model was performed to assess differences in parental resources, sense of competence, and perception of the children’s executive functions according to their condition. A path analysis model was performed to examine the impact of sense of competence and children’s condition on parental resources and children’s executive functions. Results. Parents with children with specific learning disorder reported lower scores of parental resources in terms of total scores, common antecedents, and specific antecedents compared to parents with typically developed children (total scores: MD = 56.45, p < 0.001; common antecedents: MD = 22.28, p < 0.00; specific antecedents: MD = 34.17, p < 0.001), parents with autistic children (total scores: MD = 62.79, p = 0.01; common antecedents: MD = 24.03, p = 0.01; specific antecedents: MD = 38.76, p = 0.02) and parents of children with chronic illness (total scores: MD = 37.42, p = 0.04; common antecedents: MD = 16.59, p = 0.01). The path analysis model shows a direct effect of parental satisfaction (β = 0.26) and pathology/disability (β = −0.10) on parental resources that, in turn, influence parents’ perception of their children’s executive functioning (β = 0.24). Conclusion. Although no data about the prepandemic situation is available, the current study highlights that parental stress influence children’s cognition. Moreover, parents of children with special needs seemed to be challenged during COVID-19, especially parents of children with specific learning disorders, that are already stressed out by their children’s condition. Therefore, academic services should undertake preventive measures to preserve parental well-being and to provide a supportive environment for children, especially for those with atypical development.