This work presents a Robust Stochastic Model Predictive Control (RSMPC) framework for real-time motion planning autonomous vehicles, addressing the complex multi-modal vehicle interactions. The proposed framework involves adding expert policy from observations to the dataset and applying the Data Aggregation (DAgger) method to filter unsafe demonstrations and resolve expert conflicts. A Dual-Stage Attention-based Recurrent Neural Network (DA-RNN) model is integrated to predict dual class variables from the dataset, producing a set containing constraints collision-avoidance predicted to be active. The RSMPC framework enhances formulation optimization by eliminating irrelevant collision avoidance constraints, resulting in faster control signals. The framework is applied iteratively, continuously updating observations and solving the RSMPC optimization formulation in real-time. Evaluation of the DA-RNN model achieved a recall value of 0.97 and a high accuracy rate of 98.1% in predicting dual interactions, with a minimal false negative rate of 0.026, highlighting its effectiveness in capturing interaction intricacies. Validated through simulations of interactive traffic intersections, the proposed framework demonstrably excels, showing high feasibility of 99.84% and a 15-fold increase in response speed compared to the baseline. This approach ensures autonomous vehicles navigate safely and efficiently in complex traffic scenarios, paving the way for more reliable and scalable autonomous driving solutions.