IH failures can be confounded with instruction-following failures, conflicts can be nuanced, and models can learn shortcuts such as overrefusing. We introduce IH-Challenge, a reinforcement learning training dataset, to address these difficulties. Fine-tuning GPT-5-Mini on IH-Challenge with online adversarial example generation improves IH robustness by +10.0% on average across 16 in-distribution, out-of-distribution, and human red-teaming benchmarks (84.1% to 94.1%),