We present a high-order hierarchical dynamic domain decomposition method for the Boltzmann equation based on moment realizability matrices, a concept introduced by Levermore, Morokoff, and Nadiga. This criterion is used to dynamically partition the two-dimensional spatial domain into two regimes: the Euler regime, and the kinetic regime. The key advantage of this approach lies in the use of Euler equations in regions where the flow is near hydrodynamic equilibrium, and the Boltzmann equation where strong non-equilibrium effects dominate, such as near shocks and boundary layers. This allows for both high accuracy and significant computational savings, as the Euler solver is considerably cheaper than the kinetic Boltzmann model. We propose an extension of this approach to a multi-level hierarchical dynamic domain decomposition method, in which the spatial domain is divided in three regimes: the Euler regime, an intermediate kinetic regime governed by the ES-BGK model, and the full Boltzmann regime. A coupling mechanism between regimes capable of preserving the overall high-order accuracy of both solvers Euler and kinetic is derived. All codes implement state-of-the-art numerical techniques. This combination enables robust and scalable simulations of multi-scale kinetic flows with complex geometries.