This paper presents an integrated motion planning system for autonomous vehicle (AV) parking in the presence of other moving vehicles. The proposed system includes 1) a hybrid environment predictor that predicts the motions of the surrounding vehicles and 2) a strategic motion planner that reacts to the predictions. The hybrid environment predictor performs short-term predictions via an extended Kalman filter and an adaptive observer. It also combines short-term predictions with a driver behavior cost-map to make long-term predictions. The strategic motion planner comprises 1) a model predictive control-based safety controller for trajectory tracking; 2) a search-based retreating planner for finding an evasion path in an emergency; 3) an optimization-based repairing planner for planning a new path when the original path is invalidated. Simulation validation demonstrates the effectiveness of the proposed method in terms of initial planning, motion prediction, safe tracking, retreating in an emergency, and trajectory repairing.