Renewable Energy Sources (RESs) and inverter-based technologies have become prevalent Distributed Energy Resources (DERs) within a microgrid. Unfortunately, the power supplied by RESs can be intermittent while the low quantity of rotating machine-based generation limits microgrid inertia. Without conducting power systems studies, these characteristics can lead to unacceptable system dynamics and network blackouts. System reliability is especially critical for islanded microgrids where grid support is absent. In general, power scheduling and dynamics analysis are two independently-performed power system studies despite each offering unique insights for ensuring reliability. To reap the benefits of both studies, a new approach is developed for islanded microgrids. The approach consists of a Unit Commitment (UC) model optimally scheduling power flows for an islanded microgrid, followed by a dynamic model that characterizes the network dynamics associated with each power flow transition scheduled for the microgrid. To efficiently characterize the dynamics for all power flow transitions scheduled, Dynamic Phasor (DP) modeling is proposed in the developed approach. The flexible nature and larger time-steps associated with DP modeling makes it faster than conventional transient software and suitable for analyzing islanded microgrids. Assessing the proposed approach and its sub-models with a test microgrid reveals that the proposed approach successfully performs its intended tasks of optimally scheduling power flows for an islanded microgrid and identifying transient issues associated with the power schedule. The results also reinforce the importance of both power scheduling and dynamics analysis as overvoltage is shown to appear despite the balance of supply and demand being maintained. Using the proposed approach will help microgrid owners and engineers proactively identify undesirable dynamics that need to be alleviated before the microgrid operates as planned.