Autonomous drifting is a complex challenge due to the highly nonlinear dynamics and the need for precise real-time control, especially in uncertain environments. To address these limitations, this paper presents a hierarchical control framework for autonomous vehicles drifting along general paths, primarily focusing on addressing model inaccuracies and mitigating computational challenges in real-time control. The framework integrates Gaussian Process (GP) regression with an Alternating Direction Method of Multipliers (ADMM)-based iterative Linear Quadratic Regulator (iLQR). GP regression effectively compensates for model residuals, improving accuracy in dynamic conditions. ADMM-based iLQR not only combines the rapid trajectory optimization of iLQR but also utilizes ADMM's strength in decomposing the problem into simpler sub-problems. Simulation results demonstrate the effectiveness of the proposed framework, with significant improvements in both drift trajectory tracking and computational efficiency. Our approach resulted in a 38$\%$ reduction in RMSE lateral error and achieved an average computation time that is 75$\%$ lower than that of the Interior Point OPTimizer (IPOPT).