To address slow global convergence, low search efficiency, and poor local trajectory smoothness in mobile robot path planning under complex environments with coupled static and dynamic obstacles, this paper proposes a dynamic path planning method integrating adaptive variable-step RRT* (AVS-RRT*) and an improved timed elastic band (TEB). In the global planning layer, an adaptive variable-step strategy based on local environmental complexity is designed to dynamically adjust the expansion step size according to local obstacle distribution, thereby improving search efficiency and expansion adaptability in both open and cluttered regions. A goal-biased sampling strategy and an artificial-potential-field-based heuristic, combining goal attraction, random-sample attraction, and obstacle repulsion, are further introduced to guide the tree growth toward feasible regions. In addition, a pruning strategy based on direct connection checking is adopted to reduce path redundancy and improve path quality. In the local planning layer, the global path is used as the reference trajectory, and an acceleration variation constraint is incorporated into the TEB optimization framework to suppress abrupt stop-and-go motions and velocity oscillations during dynamic obstacle avoidance, thus improving trajectory smoothness and tracking stability. Simulation and real-world experiments show that AVS-RRT* can significantly reduce computation time, the number of path nodes, and the number of iterations in environments with different complexities. Furthermore, compared with the baseline method, the proposed integrated method reduces path length by 3.91% and 3.65% and computation time by 6.89% and 7.03% in static and coupled static-dynamic environments, respectively. These results validate the effectiveness of the proposed method in improving the planning efficiency, trajectory smoothness, and navigation performance of mobile robots in complex environments.