To account for various uncertainties, such as electricity price, wind or solar output on the operation of the integrated energy system (IES), and to underscore the significance of the interplay between energy sources and loads, this paper proposes a optimisation strategy for the IES distributionally robust with multiple stakeholders. Firstly, an interactive framework for energy management and trading is introduced, integrating gas mixed with hydrogen and diversified energy storage for the Community Integrated Energy System Operator-Electric Vehicle Charging Station-Production and Sales users (CIESO-EVCS-Pros). Then, a Stackelberg game model is established to effectively exploit the demand respond capability of electric heat for EV clusters and Pros. Secondly, the Wasserstein distance is used to establish a two-layer max-min distribution robust model, based on multi-level multiple uncertainties, such as the wind power output of the upper CIESO, the price of electricity from the upper grid, and the PV output of the lower EVCS and Pros. Finally, for addressing uncertainties of both the upper and lower layers and the nonlinearity of the model, the two-layer max-min problem is transformed into a max problem by the dyadic principle, combined with the KKT condition, and the large M method. This is then condensed to a single-layer mixed-integer programming model, efficiently solved by a commercial solver. The model applicability and the validity of the proposed method are also verified by simulation analysis.