Renewable Energy Communities (RECs) play an increasingly important role in decentralized energy systems by improving local renewable energy utilization, enhancing energy flexibility, and supporting low-carbon energy transitions. However, the integration of distributed energy resources (DERs), flexible electrical loads, and energy sharing mechanisms continues to create operational and management challenges for REC-based systems. This study investigates the energy management and optimization of a residential REC in Italy composed of photovoltaic (PV) generation, battery storage systems, and flexible air-conditioning loads. A detailed optimization framework was developed to coordinate DERs and flexible demand with the objective of maximizing shared energy utilization and related economic incentives while maintaining user comfort and avoiding additional electricity costs. The regulatory framework and operational structure of RECs in Europe and Italy were also examined to support the development of the proposed management strategy. The optimization process was conducted under different operating conditions to evaluate the influence of coordinated load management on REC performance. The results showed that the coordinated control of battery storage systems and air-conditioning units improved shared renewable energy utilization and increased the economic return associated with energy sharing. The optimized operation strategy also reduced electricity costs for users while improving the operational efficiency of the community energy system. The findings indicate that advanced energy management and load coordination strategies provide an effective approach for enhancing the performance of distributed renewable energy systems and supporting the practical implementation of REC-based energy infrastructures.