Background/Objectives: Family-Centered Care (FCC) is an established standard in pediatric rehabilitation, but it has been studied almost entirely inside health services; whether its principles survive the move into community settings is largely unknown. This paper describes how caregivers perceive the family-centeredness of a community-based adapted sport program and characterizes child quality of life and caregiver well-being. Methods: Cross-sectional study within the “Skill-In” program (University of Messina). Nineteen caregivers of children with neurodevelopmental disabilities completed the MPOC-20, the KIDSCREEN-52 proxy version and the CarerQoL, analyzed with Spearman correlations and bootstrap confidence intervals. Results: The overall MPOC-20 mean item score was 5.43/7 (SD 0.83), concealing a wide spread from Respectful and Supportive Care (6.25) to Providing General Information (3.78). “Not applicable” responses (14.2%) clustered in items presupposing a clinical provider. KIDSCREEN-52 raw sums were converted to Rasch-based T-values (norm: mean 50, SD 10). Eight of ten dimensions fell within half a standard deviation of the norm, including Social Acceptance (47.65); two did not, Social Support and Peers (34.58) and Autonomy (39.42), each over one standard deviation below. Caregivers reported favorable well-being (CarerQoL-VAS 7.32/10), though six of nineteen reported no support. Associations between care processes and family outcomes were weak. Conclusions: A sport organization with no clinical mandate delivered the relational core of family-centered care comparably to rehabilitation services, while falling short on structured information. The children’s quality-of-life profile was normal on most dimensions but selectively low on peer support and autonomy. Acceptance, on this evidence, is not connection: social participation must be designed for, not assumed.