In the present study, we propose an alternative way of applying the exact factorization to the photon-electron-nuclear wavefunction building up on the encouraging developments briefly recalled above. Specifically, we decompose the problem in terms of a conditional electronic amplitude and a marginal photon-nuclear amplitude aiming (i) to study the behavior of the time-dependent potentials that drive the dynamics of the photonic and of the nuclear degrees of freedom, and (ii) to apply the coupled-trajectory mixed quantum-classical (CTMQC) algorithm, originally developed for the exact factorization of the molecular problem. Our approach treats the nuclear and the photonic degrees of freedom "on the same footing" via the marginal amplitude, thus it differs from previous work where the marginal amplitude was either the nuclear or the photonic wavefunction. As mentioned above, the idea of photonic trajectories was already investigated by other authors, however, it was done either by using the exact time-dependent potential energy surface -accessible only for model test-cases, which are exactly solvable -or by invoking the mean-field treatment within an Ehrenfest-like dynamics . Therefore, we find it interesting to perform exploratory case studies of such an alternative decomposition of the photon-electron-nuclear wavefunction and to explore the performance of CTMQC in this situation.