The optically driven coherent dynamics associated with the single-shot initialization and readout of a localized spin in a charged semiconductor quantum dot embedded in a realistic structure is theoretically studied using a new Maxwell-pseudospin model. Generalized pseudospin master equation is derived for description of the time evolution of spin coherences and spin populations in terms of the real state pseudospin coherence vector including dissipation in the system through spin-relaxation processes. The equation is solved in the time-domain self-consistently with the vector Maxwell equations for the optical wave propagation coupled to it via macroscopic medium polarization. Using the model, the long-lived electron spin coherence left behind a single resonant ultrashort optical excitation of the electron-trion transition in a charged quantum dot is simulated in the low- and high-intensity Rabi oscillation regime. Signatures of the polarized photoluminescence PL resulting from the numerical simulations, such as the appearance of a second echo pulse following the excitation and a characteristic nonmonotonic PL trace shape, specific for initial spin-up orientation, are discussed for realization of high-fidelity schemes for coherent readout of a single spin polarization state.