Persuasive social robots have the ability to influence human behaviour through social interaction, which makes them a valuable technological solution for all applications aiming to support a person's behaviour change. The recently proposed Child-Robot Relational Norm Intervention (CRNI) model introduces a new approach for persuasive social robotics, leveraging children's reluctance to disturb robots to promote behaviour change. Unlike traditional methods that rely on direct feedback or reminders, CRNI encourages children to self-monitor and self-correct improper behaviour, by making the robot express mild distress whenever the child exhibits the incorrect behaviour. This paper proposes the first implementation of the CRNI approach in a real HRI context and evaluates its effectiveness in improving children's handwriting posture. The evaluation includes two user studies: (i) a multi-session study with five children investigating the long-term impact of the approach, (ii) a controlled study with 29 children comparing CRNI to direct robot reminders. The results indicate that the CRNI model leads to more sustained posture correction compared to direct interventions. More broadly, our findings suggest that relational norm-based approaches can offer an effective yet less intrusive method for fostering positive behaviours in children.