Reconstructing dynamic scenes from Vehicle-to-Infrastructure Cooperative Autonomous Driving (VICAD) data is fundamentally complicated by temporal asynchrony: vehicle and infrastructure cameras operate on independent clocks, capturing the same dynamic agent such as cars and pedestrians at different physical times. Existing Gaussian Scene Graph methods implicitly assume synchronized observations and assign a single pose per agent per frame, which is an assumption that breaks in cooperative settings, where the resulting gradient conflicts cause severe ghosting on dynamic agents. We identify this as a representation-level failure, not an optimization artifact: we prove that any single-timeline formulation incurs an irreducible photometric loss scaling quadratically with agent velocity and cross-source time offset. To resolve this, we propose Dust (DecoUpled Spatio-Temporal) Gaussian Scene Graph for 4D Cooperative Driving Reconstruction. DUST Gaussian Scene Graph shares a canonical Gaussian set per agent for appearance consistency, while maintaining decouple pose trajectories aligned to each source's true capture timestamps. We prove that this decoupling enables the pose-gradient kernel block-diagonal, eliminating cross-source interference entirely. To make Dust practical, we further introduce a static anchor-based pose correction pipeline that corrects spatio misalignment between vehicle and infrastructure annotations, and a pose-regularized joint optimization scheme that prevents trajectory jitter and drift during early training. On 26 sequences from V2X-Seq, DUST achieves state-of-the-art performance, improving dynamic-area PSNR by 3.2 dB over the strongest baseline and reducing Fréchet Video Distance by 37.7%, with keeping robustness under larger temporal asynchrony.