Using Monte Carlo molecular dynamics simulation for a two-dimensional vortex lattice with random pinning, thermal fluctuations and vortex-vortex interactions, we study the order-disorder transition from a Bragg glass to an amorphous vortex glass or a vortex liquid in the pinning strength-temperature phase diagram. In order to determine the order in the vortex lattice, we calculate the static structure factor and evaluate the finite size exponent from the configurations of the vortex lattice. It is found that the Bragg glass region is sandwiched in between the disordered vortex glass phase at lower temperatures and the vortex liquid phase at higher temperatures, exhibiting inverse melting behavior. We attribute the unusual inverse melting behavior to the temperature dependence of the v ortex-vortex interactions.