We present a recursive path-planning method that efficiently generates a path by using reduced states of the search space and taking into account the kinematics, shape, and turning space of a car-like vehicle. Our method is based on a kinematics-aware node expansion method that checks for collisions based on the shape and turning space of a vehicle. We present two heuristics that simultaneously consider the kinematics of a vehicle with and without obstacles. In particular, for challenging environments containing complex obstacles and even narrow passages, we recursively identify intermediate goals and nodes that allow the vehicle to compute a path to its destination. We show the benefits of our method through simulations and experimental results by using an autonomous ground vehicle. Furthermore, we show that our method can efficiently generate a collision-free path for vehicles in complex environments with passageways.