[en] The aim of the present paper is the quantification of non-classical correlations between mechanical and optical modes in an optomechanical system with two spatially separated Fabry-Pérot cavities, using resolver sideband regime. To measure the amount of stationary entanglement, we use the criterion of Reid et al, while the evolution of the Gaussian quantum steering and its asymmetry make it possible to study the steerability of the correlations transfer between the different modes. Then, a theoretical study of the robustness of the Gaussian geometric discord (GGD), with respect to the temperature of the environment, is realized, for the two-mode symmetrical squeezed thermal states, to quantify quantum correlations beyond entanglement between mechanical and optical modes. By considering recent experimental parameters, we show that GGD is more robust than entanglement for a high thermal bath temperature. Finally, we find that these three indicators of quantumness enhance with the increase of the squeezing parameter. Graphical abstract: .