The effect of 2D confinement on the dynamics of the normal mode (chain mobility) and segmental relaxation in poly(propylene glycol) (PPG) has been studied with the use of broadband dielectric spectroscopy (BDS) and differential scanning calorimetry (DSC). It is shown that both processes become faster with increasing degree of confinement. Interestingly, the crossover from VFT to the Arrhenius-like behavior of chain and segmental dynamics, observed in the examined system, is strictly related to the vitrification of the adsorbed polymers. We also report that the mean relaxation times of the normal, tau(NM), and segmental modes, tau(alpha), depend on the thermal history of confined PPG and can be significantly modified using different thermal treatments. It is demonstrated that annealing of the samples below the crossover temperature, T-u, leads to a systematic shift of the segmental relaxation and normal mode toward lower frequencies, resulting in an increase in the glass transition temperature of the spatially restricted PPG. Taking into account recent studies, we allude this new experimental observation to the density equilibration: after annealing, a system with higher density characterized by more homogeneous dynamics can be obtained. It is therefore possible to modify and control the properties of the confined material by using different thermal treatment protocols. Our results offer a better understanding of the behavior of the spatially restricted soft matter and the interplay between mobilities at two completely different length scales.