Modeling and evaluation of automated vehicles (AVs) in mixed-autonomy traffic is essential prior to their safe and efficient deployment. This is especially important at urban junctions where complex multi-agent interactions occur. Current approaches for modeling vehicular maneuvers and interactions at urban junctions have limitations in formulating non-cooperative interactions and vehicle dynamics within a unified mathematical framework. Previous studies either assume predefined paths or rely on cooperation and central controllability, limiting their realism and applicability in mixed-autonomy traffic. This paper addresses these limitations by proposing a modeling framework for trajectory planning and decentralized vehicular control at urban junctions. The framework employs a bi-level structure where the upper level generates kinematically feasible reference trajectories using an efficient graph search algorithm with a custom heuristic function, while the lower level employs a predictive controller for trajectory tracking and optimization. Unlike existing approaches, our framework does not require central controllability or knowledge sharing among vehicles. The vehicle kinematics are explicitly incorporated at both levels, and acceleration and steering angle are used as control variables. This intuitive formulation facilitates analysis of traffic efficiency, environmental impacts, and motion comfort. The framework's decentralized structure accommodates operational and stochastic elements, such as vehicles' detection range, perception uncertainties, and reaction delay, making the model suitable for safety analysis. Numerical and simulation experiments across diverse scenarios demonstrate the framework's capability in modeling accurate and realistic vehicular maneuvers and interactions at various urban junctions, including unsignalized intersections and roundabouts.