It is well-known that the stabilizing control of nonholonomic systems is usually divided into two independent steps. This incurs a discontinuous switching control problem when system states start from certain regions. In light of this, we study the continuous and smooth stabilization control issues for nonlinear systems with two piecewise continuous or even smooth stabilization controllers. First, the sufficient conditions for the existence of these controllers are provided. Then, we use the controller extension method to construct some intermediate auxiliary controllers that can link the piecewise controllers given in advance continuously or even smoothly. In addition, by combining model transformation, including the cascade and fully actuated ones, with the extended state observer, we successfully employ the proposed controller extension method to solve the stabilization control of an underactuated surface ship subject to external disturbance.