Diabetes care during institutional hours is a major challenge affecting the whole family. The aim of this study was to highlight challenges and potentials regarding municipal support in relation to diabetes care of children in school, kindergarten, and daycare. The dataset consists of 80 semi-structured online interviews with 121 municipal employees from 74 (of 98) municipalities in Denmark. Data were analysed using qualitative content analysis. The analysis produced four main themes: (1) Institutional staff initially feel insecure about diabetes care responsibilities, (2) There is a high degree of parental involvement and responsibilities during institutional hours, (3) The roles of health employees vary, and (4) Fluctuating allocation of special needs assistants (SNAs) creates challenges. The findings of this nationwide qualitative study show that, even though Denmark guarantees, by law, the child’s right to support in diabetes self-care in school and childcare institutions, diabetes management in Denmark still needs to be improved, with a view to ensuring equal support for all children with diabetes.