High-fidelity simulations (HFM) of Fluid-Structure Interaction (FSI) are pivotal in engineering but remain computationally debatable for many contexts such as design optimization and uncertainty quantification. Conversely, Reduced Order Models (ROMs) offer a rapid alternative. However, standard projection-based methods (e.g., POD-Galerkin) face severe limitations in highly non-linear, turbulence-driven, or convection-dominated regimes, often referred to as the slowly decaying Kolmogorov $N$-width problem. This work introduces a numerical hybridization architecture designed to bridge this gap through a spatially adaptive multi-fidelity paradigm. The core strategy couples an ADER (Arbitrary DERivatives) solver with a Collocation-based Model Order Reduction (cMOR) method. The ADER scheme is a fully discrete space-time predictor-corrector formulation combined with dynamic mesh updating procedures. To accelerate temporal integration in smoother flow regions, the cMOR technique is applied through a hyper-reduction strategy. In particular, it restricts full HFM applications to a sparse subset of optimal collocation points, extending the local solution to the global domain via an empirical extension operator. Furthermore, this research formalize an optimal domain decomposition methodology to automate the decoposition procedure and match local fidelity levels to the specific resolution requirements of the flow dynamics. Results on the Euler equations (Laval nozzle) demonstrate the capability of this hybrid scheme to capture shock dynamics with effective reduction of computational cost.