Intersections are critical bottlenecks within urban transportation networks. Current models for simulating two-dimensional (2D) vehicular movements at intersections are met with limitations in accurately representing complex interactions and capturing vehicle dynamics. Accordingly, this paper proposes a novel microsimulation framework for trajectory planning and vehicular control at intersections. The model considers vehicle dynamics and control variables, such as acceleration and steering angle, and releases the popular assumption that there is full knowledge sharing or cooperation among vehicles at intersections. These features make the proposed framework more realistic compared to previous microsimulation attempts and applicable to traffic flow and environmental impact assessment studies. In addition, it efficiently operates in realtime for multiple vehicles, overcoming the limitations of offline methods. Moreover, the model is capable of accounting for driver/vehicle detection range, reaction time, and perception and prediction inaccuracies, which enhances its suitability for safety assessments. The evaluation in several scenarios indicates the ability of the proposed framework in realtime planning and following realistic and consistent 2D paths while avoiding collisions with other vehicles.