De-oiling hydrocyclone system is a crucial device in offshore oil and gas production. To reduce action frequency of actuators as well as energy costs, it is desired to apply event-triggered control (ETC) technique for coordination control of de-oiling hydrocyclone systems. However, the triggering errors and slugging disturbances will greatly affect oil-water separation efficiency and need to be well treated. Towards this end, this work studies the coordination control problem of de-oiling hydrocyclone systems subject to slugging disturbances and unknown system dynamics. Robust H∞ control approach is applied to reduce disturbances sensitivity and guaranteeing satisfactory oil-water separation performance. The coordination control problem is transformed into a 2-player zero-sum game problem. A model-based solution by solving the game algebraic Riccati equation (GARE) is obtained and an event-triggered (ET) off-policy reinforcement learning (RL) algorithm is developed to implement the model-based solution. The salient feature of the proposed algorithm is that the proposed model-free H∞ control method alleviates the affects of both triggering errors and slugging disturbances, which are handled together as a generalized disturbance in the algorithm. Stability and Zeno behavior avoidance of the proposed algorithm are analyzed. Simulation studies demonstrate the effectiveness of the proposed algorithm.