We propose a real-time implementable motion planning framework for cooperative object transportation by nonholonomic mobile manipulator robots (MMRs) in dynamic environments. Our global planner finds a path from start to goal through the static, obstacle-free regions in the environment and generates a set of convex, static, obstacle-free regions around the path using a novel, fast, and computationally lightweight ellipse-based technique. We introduce a nonlinear Model Predictive Control (NMPC) based real-time implementable planning technique that jointly plans feasible motion for the mobile base and the manipulator's arm and generates a kinodynamic feasible, collision-free trajectory for cooperative object transportation. Simulation and hardware experiments validate the efficiency of our proposed planning framework.