In Integrated Sensing and Communication (ISAC) networks, distributed devices can cooperate to produce radio images of the surrounding environment by exploiting phase-coherent signal processing. However, existing imaging methods are not well-suited for composite moving targets with multiple independently moving extended parts. This is due to simplistic isotropic scattering models and the lack of methods to compensate for distinct Doppler shifts from each component, which leads to image defocusing. We propose MOSAIC, the first hierarchical imaging method for composite moving targets using distributed User Equipments (UEs) and a single ISAC Base Station (BS). MOSAIC generates high-resolution images of each target part and estimates its velocity vector. Coherent imaging is performed within selected clusters of UEs observing a locally isotropic scattering from each part, while cluster-specific images are combined non-coherently across wide angles to improve the reconstruction. To mitigate Doppler-induced defocusing, Doppler components are pre-compensated before coherent imaging, turning a limitation into an additional means of resolving multiple target parts. This also enables low-complexity velocity estimation by associating Doppler frequencies across UEs. Simulations show over 50% improvement in image quality compared to existing methods, in terms of Wasserstein distance, and dm/s-level velocity estimation accuracy.