The success of a cooperative manipulation process depends on the level of disturbance rejection between the cooperating agents. However, this attribute may be jeopardized due to unexpected behaviors, such as joint saturation or internal collisions. This leads to deterioration in the performance of the manipulation task. In this paper, we present an adaptive distributed control framework that directly mitigates these internal disturbances, both in the joint (and task) spaces. With our approach, we show that including the manipulator-load coupling in the definition of the task error yields improved performance and robustness. To validate this statement, we provide stability guarantees and simulation results for two implementation cases.