Real-Time Precise Orbit Determination (RTPOD) of Low Earth Orbit (LEO) satellites relies primarily on onboard GNSS observations and may suffer from degraded performance when observation geometry weakens or tracking conditions deteriorate within satellite formations. To enhance the robustness and accuracy of RTPOD under such conditions, a cooperative Extended Kalman Filter (EKF) framework that fuses onboard GNSS and inter-satellite link (ISL) range measurements is established, integrated with an iterative Detection, Identification, and Adaptation (DIA) quality control algorithm. By introducing high-precision ISL range measurements, the strategy increases observation redundancy, improves the effective observation geometry, and provides strong relative position constraints among LEO satellites. This constraint strengthens solution stability and convergence, while simultaneously enhancing the sensitivity of the DIA-based quality control to observation outliers. The proposed strategy is validated in a simulated real-time environment using Centre National d’Etudes Spatiales (CNES) real-time products and onboard observations of the GRACE-FO mission. The results demonstrate comprehensive performance enhancements for both satellites over the experimental period. For the GRACE-D satellite, which suffers from about 17% data loss and a cycle slip ratio several times higher than that of GRACE-C, the mean orbit accuracy improves by 39% (from 13.1 cm to 8.0 cm), and the average convergence time is shortened by 44.3%. In comparison, the GRACE-C satellite achieves a 4.2% mean accuracy refinement and a 1.3% reduction in convergence time. These findings reveal a cooperative stabilization mechanism, where the high-precision spatiotemporal reference is transferred from the robust node to the degraded node via inter-satellite range measurements. This study demonstrates the effectiveness of the proposed method in enhancing the robustness and stability of formation orbit determination and provides algorithmic validation for future RTPOD of LEO satellite formations or large-scale constellations.