Objective: The aim of this study was to analyze the impact of the lack of face-to-face schooling during the COVID-19 confinement on the family quality of life of children aged 3–6 years with hemiplegia, obstetrical brachial palsy, and typical development. Materials and Methods: An observational and cross-sectional study, using an online survey hosted in Google Forms from October to December 2020, was performed in families with children with infantile hemiplegia, obstetrical brachial palsy, and typical development aged 3–6 years living in Spain. The quality of life and family impact (measured through Pediatric Quality of Life Questionnaires, PedsQL™) were evaluated, as well as the affected upper limb side, the presence of other associated problems, the parents’ job, lack of use of the affected upper limb, and the type of online intervention using different channels: phone calls, emails, and video calls. Family expectations on the treatment and on their acquired capacity to solve problems related to their children were also measured. Results: A total of 93 families participated in the study and the children’s quality of life and family impact obtained a strong correlation in three populations: infantile hemiplegia ( r = 0.844), obstetrical brachial palsy ( r = 0.513), and typical development ( r = 0.904). There was no association between quality of life and online intervention (phone calls and emails were selected), p > 0.05. Conclusion: The deprivation of schooling coupled with home confinement due to the COVID-19 pandemic had a greater impact on the quality of life of children with disabilities: infantile hemiplegia and obstetrical brachial palsy than on typically developing children and on their families. However, the online intervention did not produce improvements in quality of life, which could be a consequence of using emails or phone calls instead of video calls to interact with the families.