In this paper, we consider the multi-UAV deployment problem for a two-hop relaying system. For a better network performance, UAVs carry directional antennas that are modeled by a realistic radiation pattern. The goal is to maximize the minimum user rates, and therefore achieve fairness in the network. We propose an iterative algorithm to optimize the TDMA scheduling in both hops, UAV trajectories, antenna beamwidths, and transmit power of the base station and relays. Simulation results show the throughput improvement as a result of optimizing the directional antenna radiation patterns. In addition, we derive the optimal power allocation, which combined with the beamwidth optimization yields to a much better performance.