Due to the scalability and portability, low-altitude intelligent networks (LAINs) are essential in various fields such as surveillance and disaster rescue. However, in LAINs, unmanned aerial vehicles (UAVs) are characterized by the distributed topology and high mobility, thus vulnerable to security threats, which may degrade routing performances for data transmissions. Hence, how to ensure the routing stability and security of LAINs is challenging. In this paper, we focus on the routing with multiple UAV clusters in LAINs. To minimize the damage caused by potential threats, we present the zero-trust architecture with the software-defined perimeter and blockchain techniques to manage the identify and mobility of UAVs. Besides, we formulate the routing problem to optimize the end-to-end (E2E) delay and transmission success ratio (TSR) simultaneously, which is an integer nonlinear programming problem and intractable to solve. Therefore, we reformulate the problem into a decentralized partially observable Markov decision process. We design the multi-agent double deep Q-network-based routing algorithms to solve the problem, empowered by the soft-hierarchical experience replay buffer and prioritized experience replay mechanisms. Finally, extensive simulations are conducted and the numerical results demonstrate that the proposed framework reduces the average E2E delay by 59\% and improves the TSR by 29\% on average compared to benchmarks, while simultaneously enabling faster and more robust identification of low-trust UAVs.