When a hypersonic vehicle undergoes direct force control in the atmosphere, the interaction between the control jet and the incoming flow creates disturbance flow fields. Traditional Reynolds-averaged Navier-Stokes (RANS) models struggle to accurately predict these disturbances, leading to uncertainties. In order to deepen the understanding of the influence of supersonic side-jet inflow interference on the control system and its mechanism, a highly analytical numerical calculation method for the turbulent flow field based on the cone-pillar-skirt model is established. Comparing delayed detached eddy simulation (DDES) and RANS models under varying grid densities reveals significant discrepancies in the downstream jet wake disturbance region. DDES improves the reliability of lateral jet control results, especially under well-resolved turbulent grid conditions. Supported by simulations, the study enhances understanding of turbulent characteristics in supersonic lateral jet-induced disturbances. Dynamic DDES methods show improved pressure prediction compared to traditional RANS simulations, offering insights for enhancing the prediction accuracy of direct force control systems.