This study presents an enhanced hybrid co-simulation framework for coupled multi-domain structural analysis integrating machine learning (ML)-based surrogate models with classical numerical solvers. The proposed approach targets systems composed of multiple non-overlapping subdomains, in which some domains are resolved using pretrained neural operators, while others are analyzed via conventional finite element (FE) and rigid multibody dynamics (MBD) solvers. For partitioned multi-domain problems, an adaptive alternating procedure, built upon domain decomposition approaches, is developed to facilitate the integration of neural-operator-based subdomains through iterative exchange of physical information across subdomain interfaces. This iterative coupling scheme ensures kinematic and force consistency with enhanced residual reduction and convergence characteristics. Additionally, by leveraging pretrained DeepONet for reusable subdomains, the overall computational cost for large-scale analyses is significantly reduced while preserving the physical fidelity of the numerical solvers. The performance of the framework is assessed through several numerical examples, including both static and dynamic structural problems. The results are validated against analytical solutions and classical numerical simulations, demonstrating the computational efficiency and robustness of the proposed framework.