We explore the formation history of the Milky Way using RR Lyrae variable stars (RRLs) as fossil tracers of ancient stellar populations. The investigation focuses specifically on the Oosterhoff dichotomy, a phenomenon characterized by the separation of RRLs into two distinct groups in the Bailey diagram. The primary objective of this research is to confirm whether this dichotomy is an intrinsic feature of the Galaxy or if it was "imported" through merging events with dwarf galaxies, such as Gaia-Enceladus and Sagittarius. To test this hypothesis, chemo-dynamic classifications from existing literature were applied, analyzing their distribution in the integrals of motion space to distinguish between in situ and accreted populations. A new Period-Wesenheit-Metallicity (PWZ) relation was derived to ensure the accuracy of the distances required for the dynamical analysis. The adopted methodology relies on a robust statistical approach based on: the use of photometric parallaxes combined with Gaia astrometric data, a Bayesian MCMC (Markov Chain Monte Carlo) algorithm for parameter inference. Preliminary results indicate that the PWZ relation coefficients are consistent with current literature. Future work will involve a detailed characterization of the pulsational properties (including Fourier parameters) for each identified dynamical component, aiming to reconstruct the early evolutionary stages of our Galaxy with greater precision.