In the core of nuclear reactors, fluid-structure interaction and intense irradiation lead to the progressive deformation of fuel assemblies. When this deformation becomes significant, it can result in additional costs and extended fuel unloading and reloading operations. Therefore, it is essential to develop effective fuel management strategies that minimize excessive deformation and interactions between fuel assemblies. However, accurately predicting deformation and the interactions that arise between fuel assemblies remains challenging due to the complex interdependencies of various phenomena, including neutronics, thermal-hydraulics, and thermomechanics, each subject to inherent uncertainties. This work presents a comprehensive approach to address these challenges by focusing on the coupling between hydraulic and thermomechanical phenomena within a pressurized water reactor. An initial sensitivity analysis was conducted to determine the most influential parameters, first in hydraulic models [A. Abboud et al., BEPU 2024, 272], and then in mechanical models [A. Abboud et al., M\&C 2025, 46282]. To effectively manage uncertainties over several reactor power cycles, it is useful to have accurate surrogate models. Using this information, the coupled simulation aims to synergistically integrate hydraulic and mechanical effects, along with their interactions, to achieve a more accurate modeling of fuel assembly deformation while capturing the dependencies of each model to its uncertain parameters. Furthermore, this study goes beyond standard parameter uncertainties by addressing epistemic factors, such as the convergence algorithms and criteria used in the coupled simulations. By analyzing these coupled effects and the associated uncertainties, this work is intended to provide a deeper understanding of the interaction between hydraulic and mechanical behaviors, enhancing the reliability and accuracy of predictive simulations. Ultimately, this integrated modeling approach will help to improve reactor management by informing more robust fuel management strategies and reducing risks related to fuel assembly deformation.