Legal judgment prediction (LJP) aims to predict judicial outcomes from case facts and typically includes law article, charge, and sentencing prediction. While recent methods perform well on the first two subtasks, legal sentencing prediction (LSP) remains difficult due to its need for fine-grained objective knowledge and flexible subjective reasoning. To address these limitations, we propose $MSR^2$, a framework that integrates multi-source retrieval and reasoning in LLMs with reinforcement learning. $MSR^2$ enables LLMs to perform multi-source retrieval based on reasoning needs and applies a process-level reward to guide intermediate subjective reasoning steps. Experiments on two real-world datasets show that $MSR^2$ improves both accuracy and interpretability in LSP, providing a promising step toward practical legal AI. Our code is available at https://anonymous.4open.science/r/MSR2-FC3B.