The stable and safe operation of lithium-ion batteries is the goal of the battery management system (BMS), and the estimation of the state of charge (SOC) is one of the primary tasks of the BMS, making accurate SOC estimation a highly prominent topic over the past decade. However, existing methods inadequately integrate physical models with historical data, leading to bidirectional or unidirectional information disconnection, which poses challenges for achieving stable and precise SOC estimation. To tackle this issue, this paper proposes an enhanced Physics-Informed Neural Network (PINN) framework. The approach incorporates an additional neural network to simulate battery degradation dynamics and introduces soft constraints based on the degradation process. To effectively balance physical models and neural network, the framework includes a loss weight allocation strategy grounded in uncertainty estimation. Additionally, utilizing a dual-polarization model of the battery, supplementary features are extracted via parameter identification, further strengthening the fusion of data and model. The experimental results in the XJTU battery dataset demonstrate that the proposed method achieves a root mean square error (RMSE) of 0.0069 for SOC estimation, surpassing the performance of baseline models.