Artificial muscle-driven modular soft robots exhibit significant potential for executing complex tasks. However, their broader applicability remains constrained by the lack of dynamic model-based control strategies tailored for multi-degree-of-freedom (DOF) configurations. This paper presents a novel design of a 2-DOF robotic wrist, envisioned as a fundamental building block for such advanced robotic systems. The wrist module is actuated by twisted and coiled actuators (TCAs) and utilizes a compact 3RRRR parallel mechanism to achieve a lightweight structure with enhanced motion capability. A comprehensive Lagrangian dynamic model is developed to capture the module's complex nonlinear behavior. Leveraging this model, a nonlinear model predictive controller (NMPC) is designed to ensure accurate trajectory tracking. A physical prototype of the robotic wrist is fabricated, and extensive experiments are performed to validate its motion performance and the fidelity of the proposed dynamic model. Subsequently, comparative evaluations between the NMPC and a conventional PID controller are conducted under various operating conditions. Experimental results demonstrate the effectiveness and robustness of the dynamic model-based control approach in managing the motion of TCA-driven robotic wrists. Finally, to illustrate its practical utility and integrability, the wrist module is incorporated into a multi-segment soft robotic arm, where it successfully executes a trajectory tracking task.