This paper presents a numerical modelling methodology for an innovative installation method of floating wind turbines. The study analyses the influence of hydrodynamic and environmental modelling factors on the dynamics of a multibody system consisting of a catamaran with three wind turbines and a spar foundation with a mooring system. The research focuses on features such as viscous drag on the spar, hydrodynamic interaction between floating bodies, long- and short-crested waves, first- and second-order wave loads, wave directions, and wave peak periods. The study found that hydrodynamic modelling factors had a significant effect on the horizontal motion of the installation system but a negligible effect on vertical motion and mooring system tension. Therefore, it is recommended to consider viscous drag forces, hydrodynamic interaction, and first- and second-order wave forces when developing mechanical damping and control systems to reduce horizontal motion. The study also suggests using both long- and short-crested waves for numerical analysis when estimating the weather window for installation operability analysis. Overall, this study contributes to the development of an efficient and practical installation method for floating wind turbines by analysing the impact of hydrodynamic and environmental factors on the dynamics of the multibody system.