With increased penetration of distributed energy resources and electric vehicles (EVs), different EV management strategies can be used for mitigating adverse effects and supporting the distribution grid. This paper proposes a robust multi-objective methodology for determining the optimal day-ahead EV charging schedule while complying with unbalanced distribution grid constraints. The proposed methodology considers partially competing objectives of an EV aggregator and the respective distribution system operator, and applies a fuzzy-based mechanism for obtaining the best compromise solution. The robust formulation effectively considers the errors in the electricity price forecast and its influence on the EV schedule. Moreover, the impact of EV reactive power support on objective values and technical parameters is analysed both when EVs are the only flexible resources and when linked with other demand response programs. The method is tested on a real Danish unbalanced distribution grid with 35% EV penetration to demonstrate the effectiveness of the proposed approach. It is shown that the proposed formulation guarantees an optimal EV cost as long as the price uncertainties are lower than the aggregator’s conservativeness degree, and that EV reactive power improves local conditions without significantly affecting the EV cost.