This paper develops a more general dynamics controller to generate whole-body behaviors for a quadrupedon-wheel robot. To track the quadruped centroidal motion, the wheeled motion is achieved by combining the wheel contact constraints and the centroidal momentum/dynamics model. The dynamics controller is based on a new hybrid hierarchical and prioritized weighted optimization framework. We propose one concept of a recursively updated dynamics model and this model enables to integrate the new prioritized weighted scheme in the hierarchical framework. In contrast with the conventional weighted scheme, we propose to use null-space projections among its sub-tasks. Then the prioritized impedance controller is proposed and integrated in our dynamics model, which enables to influence the hierarchical and prioritized weighted tasks in a decoupled way. The task accelerations in the two schemes are extracted with quadratic forms depending on the actuated torque and the prioritized impedance force using null-space based inverse dynamics. The inequality constraints are modified to ensure the compatibility with the hybrid convex optimization. This dynamics controller is more general and its algorithm is given completely which enables our robot to track the centroidal motion on rough terrain and handle other missions in three simulation scenarios.