Modern supply chains face unprecedented vulnerability to disruptions arising from natural disasters, infrastructure failures, demand volatility, and geopolitical instability. The Dynamic Multi-Depot Vehicle Routing Problem with Disruptions (DMDVRP-D) captures the complexity of real-time logistics re-optimization when such events occur, yet existing solution approaches inadequately balance computational efficiency with solution resilience. This paper proposes the Dynamic Resilient Supply-chain Optimizer (DRSO), a novel hybrid metaheuristic that integrates Adaptive Large Neighborhood Search (ALNS) with Grey Wolf Optimizer (GWO) for solving the DMDVRP-D. DRSO introduces five key innovations: 1) scenario-tree-based stochastic programming embedded within fitness evaluation to account for disruption uncertainty, 2) ALNS destroy-repair operators specialized for supply chain resilience, including Facility Substitution (FS), Emergency Re-Routing (ER), Demand Splitting (DS), and Multi-Modal Switching (MS), 3) GWO-guided intensification on promising ALNS neighborhoods to accelerate convergence, 4) real-time re-optimization triggered by disruption events with warm-start from pre-disruption solutions, and 5) a Composite Resilience Score (CRS) metric that unifies Recovery Time (RT), Service Level (SL), and Excess Cost (EC) into a single evaluative measure. We formulate the DMDVRP-D as a Mixed-Integer Linear Program (MILP) and evaluate DRSO on modified Solomon VRPTW benchmark instances extended with disruption scenarios, as well as two real-world case studies: a Nigerian pharmaceutical distribution network spanning the Lagos–Abuja–Kano corridor (45 nodes) and a Chinese manufacturing supply chain in the Yangtze River Delta (YRD) region (78 nodes). Computational experiments over 30 independent runs demonstrate that DRSO achieves 18–32% lower disruption recovery cost, 25–41% faster RT, and 15–28% fewer unserved customers compared to standalone ALNS, Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and commercial solver (Gurobi with time limit). Statistical significance is confirmed via the Wilcoxon signed-rank test at p < 0.05. The results establish DRSO as a competitive and practical approach for resilient supply chain routing under dynamic disruption conditions.