Electrification of private transportation and residential heating is a potential action to decrease significantly carbon emissions. However, the lack of coordination of such emerging loads can increase stress on the power distribution grid. To this end, this paper proposes a two-stage energy management strategy, to enhance the flexibility of energy communities. First, an optimization algorithm-based model predictive control (MPC) is developed for home energy management systems (HEMS) to schedule electric vehicles (EVs) for charging and discharging in cooperation with heat pump and thermal energy storages. The objective is to reduce electricity bills and EV battery degradation costs while maintaining thermal demand. Second, the predictive coordination based on the nonlinear AC optimal power flow approach is applied to enhance the grid flexibility under a community energy management system scheme. To validate the performance of the proposed method, we develop a co-simulation framework by implementing the optimization algorithm and simulation scenarios in a Python Environment and modelling the electricity grid in the PowerFactory-DIgSILENT, which are linked together. Extensive numerical simulations are carried out under the active demand response program-based hourly electricity pricing and different weather data in Sweden. The results show that the proposed method can reduce operating costs and enhance the energy flexibility of the energy community. Moreover, it can decrease the stress on the community power grid and prevent load-shedding events compared to the non-predictive coordinated method.