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Chemistry under the conditions of vibrational strong coupling has recently attracted major attention from different experimental and theoretical groups alike. In particular, low-dimensional model systems have shed light on the possible formation mechanisms of vibrational polaritons and their dynamics in microcavities subject to the possible influence of external excitations. In the present contribution, the polaritonic states obtained by placing a Hénon-Heiles (HH) 2D model inside a microcavity and their dynamics are theoretically investigated. Oblique coordinates, as introduced by Zuñiga and co-workers J. Phys. B: At., Mol. Opt. 50, 025101 (2017), allow the accurate determination of polaritonic eigenstates, assuming the lowest fundamental mode of the HH model to be in resonance with a single cavity mode. Very different regimes for the polariton dynamics are found depending on whether the two vibrational modes of the model are themselves involved in a Fermi resonance or not. In the former case, the flow between photonic and vibrational modes appears mostly regular under molecular times scales and exhibits maximum efficiency near coupling strengths corresponding to avoided crossings in the polaritonic eigenstates. When the two HH modes are in the 1:2 ratio, the dynamics is much less regular but promotes intramolecular vibrational redistribution, although with a greater sensitivity toward initial conditions.