Environmental policies are pushing cross-sector electrification, including the transport and heating sectors. However, the large integration of distributed energy resources, such as electric vehicles (EV), heat pumps (HP), and photovoltaic (PV) systems, has a strong influence on the stability of low voltage (LV) distribution grids and can lead to high reinforcement costs. This work develops a methodology to quantify the impacts of a joint integration of EVs, PV, and HPs into LV distribution grids and the ability of a decentralized EV smart charging strategy to reduce the constraints. A central occupancy model generates demand and generation profiles for the studied technologies, which are then used to carry out Monte Carlo simulations for unbalanced power flow analysis of LV grids. A case study of a typical Belgian rural grid shows that the main impacts arise from HP integration, creating voltage deviations and transformer overloading. EV integration impacts are less significant, creating grid issues only at high-penetration levels and to a lesser extent than HPs. The proposed smart charging strategy allows reducing the impacts of EV integration; however, it does not allow increased penetration of the other technologies. Other smart charging and Vehicle-to-Grid (V2G) strategies should be analyzed to further increase DER penetration.