Using the resistively shunted junction model, we study the magnetic frustration induced dynamic melting transitions of a current-driven vortex system in two-dimensional weakly disordered Josephson juction arrays at zero temperature and very low temperatures. From the unified model simulations, we simultaneously obtain two kinds of dynamic melting transitions of the vortex flow, just below the vortex glass phase and above a dynamic melting threshold, respectively. The reenter pinned dilute vortex liquid behavior and the intrinsic quantum vortex liquid ͑QVL͒ phenomenon are also obtained, consistent with the recent experimental reports in disordered and superconducting MoGe films. The peak effect of critical current in the vortex glass is induced by intrinsic collective pinning effects in the plastic flow and the enhancement of critical current and voltage noise in the QVL phase arises from intrinsic quantum fluctuations in the moving vortex flow.