Nonholonomic mechanical systems encompass a large class of practically interesting robotic structures, such as wheeled mobile robots, space manipulators, and multi-fingered robot hands. However, few results exist on the cooperative control of such systems in a generic, distributed approach. In this work we extend a recently developed distributed \ac{IDA-PBC} method to such systems. More specifically, relying on port-Hamiltonian system modelling for networks of mechanical systems, we propose a full-state stabilization control law for a class of nonholonomic systems within the framework of distributed \ac{IDA-PBC}. This enables the cooperative control of heterogeneous, underactuated and nonholonomic systems with a unified control law. This control law primarily relies on the notion of Passive Configuration Decomposition and a novel, non-smooth control law proposed here. A low-level collision avoidance protocol based on the \ac{APF} method is also implemented in order to achieve dynamic inter-agent collision avoidance, enhancing the practical relevance of this work. Theoretical results are tested in different simulation scenarios in order to highlight the applicability of the derived method.