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We present an efficient numerical method for earthquake sequences in 2D antiplane shear that incorporates wave propagation. A vertical strike‐slip fault governed by rate‐and‐state friction is embedded in a heterogeneous elastic half‐space discretized using a high‐order accurate Summation‐by‐Parts finite difference method. Adaptive time‐stepping is applied during the interseismic periods; during coseismic rupture we apply a non‐stiff method, enabling a variety of explicit time stepping methods. We consider a shallow sedimentary basin and explore sensitivity to spatial resolution and the switching criteria used to transition between solvers. For sufficient grid resolution and switching thresholds, simulations results remain robust over long time scales. We explore the effects of full dynamics and basin depth and stiffness, making comparisons with quasi‐dynamic counterparts. Fully‐dynamic ruptures generate higher stresses, faster slip rates and rupture speeds, producing seismic scattering in the bulk. Because single‐event dynamic simulations penetrate further into sediments compared to the quasi‐dynamic simulations, we hypothesize that the incorporation of inertial effects would produce sequences of only surface‐rupturing events. However, we find that subbasin ruptures can still emerge with elastodynamics, for sufficiently compliant basins. We also find that full dynamics can increase the frequency of surface‐rupturing events, depending on basin depth and stiffness. These results suggest that an earthquake's potential to penetrate into shallow sediments should be viewed through the lens of the earthquake sequence, as it depends on basin properties and wave‐mediated effects, but also on self‐consistent initial conditions obtained from seismogenic cycling. Plain Language Summary: We have developed a robust and efficient modeling framework for simulating earthquake sequences that incorporates the important physics of seismic waves and heterogeneous materials. We consider earthquakes occurring on a strike slip fault cutting through a sedimentary basin and show that long‐term modeling outcomes are sensitive to the numerical parameters of grid resolution and how we switch between solvers for the interseismic and coseismic phases. In addition, we compare fully‐dynamic and quasi‐dynamic model outcomes and show that when full dynamics are present, ruptures are much larger. If the basin contains sufficiently soft materials, some events can remain buried below the sedimentary basin, as in the quasi‐dynamic scenario, however full‐dynamics can increase the frequency of events the rupture all the way to Earth's surface. These results underscore the importance that earthquake rupture behavior is strongly dependent on both basin properties and initial conditions that have evolved over very long periods (∼1000s of years). Key Points: Non‐stiff summation‐by‐parts finite difference methods can be derived for fully‐dynamic earthquake sequences with rate‐and‐state frictionLong‐term simulations of fully‐dynamic earthquake sequences are sensitive to the switching criterion even with adequate resolutionFor sufficiently compliant basins, subbasin ruptures can still emerge with full elastodynamics [ABSTRACT FROM AUTHOR]