Multi-parameter quantum estimation serves as the core of precision metrology and distributed quantum sensing networks, enabling the simultaneous acquisition of multidimensional physical quantities. However, quantum resources are extremely sensitive to environmental decoherence. In practical open systems, unavoidable photon losses not only degrade the quantum entanglement but also disrupt the resource allocation structures within multi-parameter networks. This severely restricts the robustness and practical applications of quantum sensing technologies. To address this structural vulnerability, we propose a two-parameter joint estimation scheme utilizing continuous-variable three-mode Greenberger-Horne-Zeilinger (GHZ) entangled states. Global multipartite entanglement is generated using independent optical parametric amplifiers (OPAs) and specifically designed linear beam-splitter networks, coupled with a tailored joint homodyne detection strategy. We establish a comprehensive linear environment coupling model incorporating both channel transmission and terminal detection losses. Quantitative evaluations demonstrate that under ideal lossless conditions, the estimation sensitivities for both parameters simultaneously surpass the Standard Quantum Limit (SQL) and saturate the Quantum Cramér-Rao Bound (QCRB). Notably, the signal-to-noise ratio of phase estimation achieves a significant enhancement of 19.62 dB with an input squeezing parameter of 1.50 even in lossy environments. Crucially, our in-depth analysis reveals the distinct underlying mechanisms of different loss types. While symmetric loss uniformly introduces vacuum noise that gradually attenuates quantum correlation and limits the sensitivity gain from high initial squeezing, asymmetric loss fundamentally destroys the symmetric distribution of global entanglement resources. This destruction triggers a sharp divergence in the two-parameter estimation sensitivities, causing the precision of specific parameters to degrade drastically below the classical limit. This study elucidates the intrinsic restriction mechanism of quantum resource distribution on multi-parameter sensing performance. We conclude that maintaining channel symmetry is as vital as improving transmittance, thereby providing a comprehensive theoretical basis and optimization guidelines for designing next-generation distributed quantum sensing networks under practical non-ideal conditions.