Mobile Ad Hoc Networks (MANETs) face critical challenges of unstable routes, dynamic topology, and security vulnerabilities caused by rogue nodes. This paper proposes AODV-KC, a secure and adaptive routing protocol that integrates link expiration time (LET)-based route stability metrics, AES-256-GCM authenticated encryption, and a trust-driven intrusion detection mechanism. The protocol dynamically learns reliable paths using reinforcement learning by considering link quality, residual energy, and trust scores, while isolating malicious behaviors such as packet dropping, blackhole, grayhole, impersonation, and TC flooding. Simulation results in NS-2 demonstrate that AODV-KC achieves up to 31.5% higher packet delivery ratio, 35.2% lower packet loss, 29.9% reduced delay, and 31.5% improved throughput compared to baseline schemes, with only marginal cryptographic overhead. These findings confirm that AODV-KC offers a scalable and energy-efficient solution for secure, stable, and high-performance routing in dynamic MANET environments.