In this manuscript, a scheme for neural-learning-enhanced Cartesian Admittance control is presented for a robotic manipulator to deal with dynamic environments with moving remote center of motion (RCM) constraints. Although some research has been implemented to address fixed constrained motion, the dynamic moving movement constraint is still challenging. Indeed, the moving active RCM constraints generate uncertain disturbance on the robot tool shaft with unknown dynamics. The neural-learning-enhanced decoupled controller with disturbance optimisation is employed and implemented to maintain the performance under the kinematic uncertain and dynamic uncertain generated. In addition, the admittance Cartesian control method is introduced to control the robot, providing compliant behaviour to an external force in its operational space. In this proposed framework, a neural-learning-enhanced disturbance observer is investigated to calculate the external factor operating on the end effector premised on generalised momentum in order to ensure accuracy. Finally, the experiments are implemented using a redundant robot to validate the efficacy of the suggested approach with moving RCM constraints.