The increasing penetration of intermittent renewable energy into the power grid introduces significant operational challenges. A promising solution involves integrating the power grid with electric vehicles (EVs), leveraging their ability to store electricity and contribute to grid operations through vehicle-to-grid (V2G) technology. In this paper, we consider a grid-vehicle integration (GVI) system employing V2G while managing uncertainties in renewable generation, power load, and EV trip demand. We formulate the problem of operating a GVI system as a two-stage robust mixed-integer program. In the first stage, the grid operator, aiming to minimize the worst-case total cost, decides whether to start up a generator. In the second stage, the grid decides power generation levels and charging/discharging interactions with EVs to satisfy the power load. Meanwhile, the mobility operator utilizes the EV fleet to fulfill the interactions and satisfy EV trip demands. The inherent complexity arising from discrete decisions, uncertainties, and robustness requirements poses a significant computational challenge, prompting the proposal of a machine learning-driven optimization approach. Our approach outperforms benchmarks in computational time and solution quality for large-scale real instances. We reveal that V2G can reduce the number of required generators and stabilize power generation by “filling” the low power load and “shaving” the peak. The V2G helps achieve a substantial 21.66% average reduction in carbon emissions compared to the case without V2G. Such impact is more pronounced under a bimodal power load pattern than a unimodal pattern. Finally, achieving carbon neutrality in this integration system is feasible yet challenging.