Task and Motion Planning (TAMP) integrates high-level task planning with low-level motion feasibility, but existing methods are costly in long-horizon problems due to excessive motion sampling. While LLMs provide commonsense priors, they lack 3D spatial reasoning and cannot ensure geometric or dynamic feasibility. We propose a kinodynamic TAMP planner based on a hybrid state tree that uniformly represents symbolic and numeric states during planning, enabling task and motion decisions to be jointly decided. Kinodynamic constraints embedded in the TAMP problem are verified by an off-the-shelf motion planner and physics simulator, and a VLM guides exploring a TAMP solution and backtracks the search based on visual rendering of the states. Experiments on the simulated domains and in the real world show 32.14% - 1166.67% increased average success rates compared to traditional and LLM-based TAMP planners and reduced planning time on complex problems, with ablations further highlighting the benefits of VLM backtracking. More details are available at https://graphics.ewha.ac.kr/kinodynamicTAMP/.