Reconstructing dynamic driving scenes is essential for developing autonomous systems through sensor-realistic simulation. Although recent methods achieve high-fidelity reconstructions, they either rely on costly human annotations for object trajectories or use time-varying representations without explicit object-level decomposition, leading to intertwined static and dynamic elements that hinder scene separation. We present IDSplat, a self-supervised 3D Gaussian Splatting framework that reconstructs dynamic scenes with explicit instance decomposition and learnable motion trajectories, without requiring human annotations. Our key insight is to model dynamic objects as coherent instances undergoing rigid transformations, rather than unstructured time-varying primitives. For instance decomposition, we employ zero-shot, language-grounded video tracking anchored to 3D using lidar, and estimate consistent poses via feature correspondences. We introduce a coordinated-turn smoothing scheme to obtain temporally and physically consistent motion trajectories, mitigating pose misalignments and tracking failures, followed by joint optimization of object poses and Gaussian parameters. Experiments on the Waymo Open Dataset demonstrate that our method achieves competitive reconstruction quality while maintaining instance-level decomposition and generalizes across diverse sequences and view densities without retraining, making it practical for large-scale autonomous driving applications. Code will be released.