In view of the weak energy supply stability of the single regional integrated energy system (RIES), the ability to deal with uncertainties is poor. To solve the problem of equilibrium optimization among system economy, robustness and efficiency, this paper interconnects multiple RIES with different resource to form multi-RIES through peer-to-peer energy trading. The control strategy of energy interactive operation involving multiple RIES is optimized. Using the uncertainty confidence set of renewable energy to depict the uncertainty on the source side, a two-stage distributed robust optimal control model for RIES based on data-driven is proposed, and the column and constraint generation (C&CG) algorithm is adopted to significantly improve the solution efficiency. Then, a multi-RIES cooperative game model with uncertain scenarios is proposed, and according to this model, a coupled C&CG-alternating direction multiplier method (ADMM) algorithm is proposed, which realizes the privacy protection of RIES and makes the system have good convergence performance. Finally, the case analysis proves that the strategy proposed in this paper can not only realize energy coordination and complementarity among multiple RIES, but also improve the stability of the system operation and significantly reduce the dependence of the system on the distribution network.