This work investigates the problem of tangential velocity estimation in automotive radar systems, addressing the limitations of conventionally considered models. Conventional automotive radars are usually based on far-field models and estimate the target's range, radial velocity, and direction-of-arrival (DOA) but are not able to estimate the tangential component of the target 2-D velocity, which is a critical parameter for reliable perception of dynamic environments. To address this challenge, we introduce the near-field radar model, which considers various migration elements in range, radial velocity, and Doppler along time and space. Conventionally, these migration effects result in smearing of the likelihood function for estimating the target parameters. However, if the model is correctly specified, these migration effects are informative for tangential velocity estimation. We conduct an identifiability analysis for tangential velocity estimation using the Cramér-Rao bound and ambiguity function. The insights from this study motivate the use of a separated array configuration and the development of a computationally efficient maximum likelihood based algorithm designed to utilize target migrations for tangential velocity estimation, while maintaining practical computational complexity. In addition to tangential velocity estimation, the proposed algorithm mitigates likelihood smearing in range, radial velocity, and Doppler. Simulations validate the theoretical feasibility study, and evaluate the algorithms' performance in both single- and multi-target scenarios. The proposed approach improves the accuracy and reliability of automotive radars, enhancing situational awareness for advanced driver assistance systems and autonomous vehicles.