In this study, we employ direct numerical simulation (DNS) to investigate the solutal hydrodynamics dictating the three-dimensional coalescence of microscopic, identical-sized sessile drops of different but miscible shear-thinning polymeric liquids (namely, PVAc or polyvinyl acetate and PMMA or polymethylmethacrylate), with the drops being in partially wetted configuration. Despite the ubiquitousness of the interaction of different dissimilar droplets in a variety of engineering problems ranging from additive manufacturing to understanding the behavior of photonic crystals, coalescence of drops composed of different polymeric and non-Newtonian materials has not been significantly explored. Interaction of such dissimilar droplets often involves simultaneous drop spreading, coalescence, and mixing. The mixing dynamics of the dissimilar drops are governed by interphase diffusion, the residual kinetic energy of the drops stemming from the fact that coalescence starts before the spreading of the drops have been completed, and the solutal Marangoni convection. We provide the three-dimensional velocity fields and velocity vectors inside the completely miscible, dissimilar coalescing droplets. Our simulations explicate the relative influence of these different effects in determining the flow field at different locations and at different time instances and the consequent mixing behavior inside the interacting drops. We also show the non-monotonic (in terms of the direction of migration) propagation of the mixing front of the miscible coalescing drops over time. We also establish that the overall mixing (on either side of the mixing front) speeds up as the Marangoni effects dictate the mixing. We anticipate that our study will provide an important foundation for studying miscible multi-material liquid systems, which will be crucial for applications such as inkjet or aerosol jet printing, lab-on-a-chip, polymer processing, etc.