The Large High Altitude Air Shower Observatory (LHAASO) has recently reported five Galactic microquasars as Ultra-High-Energy (UHE) gamma-ray emitters (> 100 TeV). Among these sources, the microquasar V4641 Sgr exhibits gamma-ray emission up to $\sim$0.8 PeV, requiring the acceleration
of particles to multi-PeV energies, as well as the hardest UHE spectrum. The mechanisms behind particle acceleration to such energies are not well understood. Furthermore, the limited multi-wavelength (MWL) information on this source appears contradictory, further complicating interpretation and suggesting that V4641 Sgr may represent a particularly unusual case. In this work, we present a detailed physical model of V4641 Sgr that combines first-principles simulations of stochastic (turbulent) particle acceleration with MWL emission modeling. We adopt a leptonic scenario in which electrons are accelerated via the second-order Fermi process
driven by relativistic strong turbulence ($\delta B/B \sim 1$). The particle energization is simulated using a dedicated Monte Carlo framework STRIPE that incorporates the effects of intermittent energy gains and radiative losses. The resulting accelerated electrons produce UHE γ-rays through inverse Compton scattering on both the cosmic microwave background (CMB) and the interstellar radiation fields (ISRF). Our model is capable of reproducing key observational characteristics
of the system, including particle acceleration to energies of tens of PeV, as well as the TeV-PeV gamma-ray spectrum and the hard spectral index measured by LHAASO. Nonetheless, several aspects remain unresolved, highlighting the need for deeper observational coverage and further theoretical
refinement.