In the context of autonomous driving systems, SLAM and dynamic object tracking represent pivotal challenges. Autonomous driving scenarios frequently demand the simultaneous acquisition of ego-pose and comprehensive motion information from the surrounding environment to enhance decision-making and scene comprehension.Given the inherent interdependence between these two challenges, a viable approach is to integrate SLAM and object tracking into an interconnected system referred to as SLAMMOT. However, many conventional SLAMMOT solutions rely on a single motion model for object tracking, which may inadequately capture complicated dynamics of real-world motions. In practice, object motion patterns can change from time to time, not conforming neatly to a single model. To handle existing challenges, this paper proposes the IMM-SLAMMOT, a tightly-coupled LiDAR-based SLAMMOT system that utilizes instance semantic segmentation and IMM modelling for dynamic object tracking. Ego-pose and dynamic object states are jointly optimized in an innovative graph optimization framework intimately integrated with the IMM algorithm. Comparative analysis against our baseline, which employs a single motion model for object tracking, demonstrates that the IMM-SLAMMOT outperforms at motion-pattern-transition moments and consistently achieves competitive results in SLAM and multi-object tracking tasks throughout the entire trajectory.