The hose–drogue system is highly sensitive to aerodynamic disturbances and aircraft maneuvers during aerial refueling, posing risks to operational safety. This paper develops a multibody dynamic model based on the absolute nodal coordinate formulation (ANCF), incorporating standard atmospheric models, tanker wake effects, and a compliant penalty-based drogue–probe constraint. The transient responses to tanker roll/pitch maneuvers and receiver vertical disturbances are systematically analyzed. Our findings clarify the nonlinear dynamics of the hose–drogue system considering tanker/receiver's attitude changes and provide a foundation for structural risk assessment and control design.