Adaptation is essential for biological motor control, enabling rapid modifications of control strategies as the environment changes. However, we still lack a unified network-level theory of coordinated motor adaptation. In previous work, we have proposed a multi-area RNN capable of rapid motor adaptation. The network comprises an internal forward model and a planning/control policy network, both of which are continuously modulated by a network that performs contextual inference. The network is meta-trained to maintain proficient control of hand reaches in the face of changing environmental dynamics (force fields, FF). Behaviorally, the network exhibits successful few-shot learning of new contexts, with both state estimation and motor preparation/control improving rapidly within few interactions with the environment. Here, we examine the neural dynamics of adaptation in our multi-area network. First, we observe a systematic reorganization of preparatory activity following FF changes. The ring-structured manifold of preparatory states associated with center-out reaching targets rotates in a way consistent with compensatory re-aiming, an effect most pronounced for reach directions close to the adapted direction. Moreover, adaptation causes this ring manifold to shift along a third dimension that separates the various FF contexts. These findings closely align with experimental data from monkey primary motor cortex, and are not observed in a control architecture composed of a single large RNN. More generally, our model makes the testable prediction that the neural representations of movement targets and motor context should be approximately separable, not only during motor preparation but also during execution. Our model provides a promising framework for integrating neural and behavioral data to advance our understanding of adaptive motor control.