Neglecting the impact of time-varying parameters, such as pressure angle and backlash induced by gear radial displacement, inevitably results in unclear research on dynamic analysis of the planetary gear transmission system. To address these issues, our paper presents a new translational-torsional nonlinear dynamic model for a two-stage 2K-H planetary gear set considering the time-varying characteristics of mesh parameters and backlash, as well as the effects of transmission errors, time-varying mesh stiffness (TVMS), and eccentricity among other sources of excitation. By deriving the system equation using the Lagrange method and solving it through numerical integration, our study explores the influence of time-varying mesh parameters on the dynamic response of the system. In addition, the nonlinear dynamic characteristics of the planetary transmission system are revealed employing the phase trajectories, Poincaré maps and bifurcation diagrams.