Multiple object tracking (MOT) techniques can help to build gate-free parking lot management systems purely under vision-based surveillance. However, conventional MOT methods tend to suffer long-term occlusion and cause ID switch problems, making applying them directly in crowded and complex parking lot scenes challenging. Hence, we present a novel disentanglement-based architecture for multi-object detection and tracking to relieve the ID switch issues. First, a background image is disentangled from the original input frame; then, MOT is applied separately to the background and original frames. Next, we design a fusion strategy that can solve the ID switch problem by keeping track of the occluded vehicles while considering complex interactions among vehicles. In addition, we provide a dataset with annotations in severe occlusions parking lot scenes that suits the application. The experiment results show our superiority over the state-of-the-art trackers quantitatively and qualitatively.