Social robots offer promising possibilities for special education, particularly in supporting children with complex neurodevelopmental disorders (NDDs) who often experience learning difficulties, such as challenges with handwriting skills. However, most studies to date have been short-term and conducted in controlled lab settings. This study presents a robot-assisted intervention using a Wizard of Oz interface, the R2C3 system (Rehabilitation Robotic Companion for Children and Caregivers), to support handwriting reeducation in a real, long-term educational setting. The intervention adopted a learning-by-teaching scenario involving 18 children with NDD and dysgraphia, alongside 8 caregivers (teachers or occupational therapists), who participated in 9 handwriting-focused sessions facilitated through a serious game. Results showed strong engagement with low attrition (2 dropouts) and substantial improvement: 73.3 % of children improved their handwriting scores by at least one standard deviation on the BHK test. Improvement was significantly associated with engagement in the game and the nature of verbal exchanges, emphasizing the social robot's role in the design of our sessions. In a subsample of 11 children, sessions with the R2C3 system were compared with a session where the robot operated autonomously with minimal behaviors, further underscoring the impact of the robot's proactive behaviors on engagement and outcomes.