  Interacting central spin systems, in which a central spin is coupled to a
strongly correlated spin bath with intrabath interaction, consist of an
important class of spin systems beyond the usual Gaudin magnet. These systems
are relevant to several realistic setups and serve as an interesting platform
to study interaction controlled decoherence and frustration induced instability
of magnetic order. Using an equations-of-motion method based on analytical
representations of spin-operator matrix elements in the XX chain, we obtain
exact long-time dynamics of a generalized Heisenberg star consisting of a
spin-$S$ central spin and an inhomogeneously coupled XXZ chain of $N\leq 16$
bath spins. In contrast to previous studies where the central spin dynamics is
mainly concerned, we focus on the influence of the central spin on the dynamics
of magnetic orders within the spin bath. By preparing the XXZ bath in a N\'eel
state, we find that in the gapless phase of the bath even weak system-bath
coupling could lead to nearly perfect relaxation of the antiferromagnetic
order. In the gapped phase, the staggered magnetization decays rapidly and
approaches a steady value that increases with increasing anisotropy parameter.
These findings suggest the possibility of controlling internal dynamics of
strongly correlated many-spin systems by certain coupled auxiliary systems of
even few degrees of freedom. We also study the dynamics of the R\'enyi
entanglement entropy of the central spin when the bath is prepared in the
ground state. Both the overall profile and initial growth rate of the R\'enyi
entropy are found to exhibit minima at the critical point of the XXZ bath.
