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Collisionless magnetic reconnection typically requires kinetic treatments that are, in general, computationally expensive compared to fluid-based models. In this study, we use the magnetohydrodynamics with adaptively embedded particle-in-cell (MHD-AEPIC) model to study the interaction of two magnetic flux ropes. This innovative model embeds one or more adaptive PIC regions into a global MHD simulation domain such that the kinetic treatment is only applied in regions where kinetic physics is prominent. We compare the simulation results among three cases: 1) MHD with adaptively embedded PIC regions, 2) MHD with statically (or fixed) embedded PIC regions, and 3) a full PIC simulation. The comparison yields good agreement when analyzing their reconnection rates and magnetic island separations, as well as the ion pressure tensor elements and ion agyrotropy. In order to reach a good agreement among the three cases, large adaptive PIC regions are needed within the MHD domain, which indicates that the magnetic island coalescence problem is highly kinetic in nature where the coupling between the macro-scale MHD and micro-scale kinetic physics is important.