Due to their ability to adapt to different terrains, quadruped robots have drawn much attention in the research field of robot learning. Legged mobile manipulation, where a quadruped robot is equipped with a robotic arm, can greatly enhance the performance of the robot in diverse manipulation tasks. Several prior works have investigated legged mobile manipulation from the viewpoint of control theory. However, modeling a unified structure for various robotic arms and quadruped robots is a challenging task. In this paper, we propose a unified framework disturbance predictive control where a reinforcement learning scheme with a latent dynamic adapter is embedded into our proposed low-level controller. Our method can adapt well to various types of robotic arms with a few random motion samples and the experimental results demonstrate the effectiveness of our method.