This paper develops an effective, cooperative, and probabilistically-complete multi-robot motion planner. The approach takes into account geometric and differential constraints imposed by the obstacles and the robot dynamics by using sampling to expand a motion tree in the composite state space of all the robots. Scalability and efficiency is achieved by using solutions to a simplified problem representation that does not take dynamics into account to guide the motion-tree expansion. The heuristic solutions are obtained by constructing roadmaps over low-dimensional configuration spaces and relying on cooperative multi-agent graph search to effectively find graph routes. Experimental results with second-order vehicle models operating in complex environments, where cooperation among the robots is required to find solutions, demonstrate significant improvements over related work.