To more accurately capture vehicle-following behavior in freeway diversion areas, this study proposes an enhanced car-following model by incorporating a lane-changing pressure gain factor into the full velocity difference model (FVDM). The proposed model accounts for both lane-changing pressure and lane-changing behavior. First, a linear stability analysis reveals that the stability region of the freeway diversion area diminishes as the lane-changing pressure gain factor increases. Second, using trajectory data from 92 lane-changing vehicles extracted from the NGSIM dataset, the improved car-following model is calibrated and validated. Simulation results demonstrate that the improved model more accurately reproduces vehicle speed and position. Compared with the original FVDM, the simulation error of the proposed pressure-based FVDM (P-FVDM) is reduced by 16%. Compared with the lane pressure FVDM(LP-FVDM), the proposed pressure-lane pressure FVDM(PLP-FVDM) reduces error by 12%. Finally, the improved model is used to simulate traffic oscillation in the diversion area. Results show that lane changing behavior can trigger traffic oscillations. Higher driving speeds attenuate oscillation amplitudes, while lower speeds result in a concave growth pattern of speed standard deviation along the vehicle platoon in the upstream direction. Furthermore, lane changes occurring closer to the exit ramp exacerbate oscillations, whereas shorter lane-changing duration help suppress them.