Optimal allocation of shared resources is key to deliver the promise of jointly operating radar and communications systems. In this paper, unlike prior works which examine synergistic access to resources in colocated joint radar-communications or among identical systems, we investigate this problem for a distributed system comprising heterogeneous radars and multi-tier communications. In particular, we focus on resource allocation in the context of multi-target tracking (MTT) while maintaining stable communication connections. By simultaneously allocating the available power, dwell time and shared bandwidth, we improve the MTT performance under a Bayesian tracking framework and guarantee the communications throughput. Our alternating allocation of heterogeneous resources (ANCHOR) approach solves the resulting nonconvex problem based on the alternating optimization method that monotonically improves the Bayesian Cram\'er-Rao bound. Numerical experiments demonstrate that ANCHOR significant improves the tracking error over two baseline allocations and stability under different target scenarios and radar-communications network distributions.