In recent years, drones have found increased applications in a wide array of real-world tasks. Model predictive control (MPC) has emerged as a practical method for drone flight control, owing to its robustness against modeling errors/uncertainties and external disturbances. However, MPC's sensitivity to manually tuned parameters can lead to rapid performance degradation when faced with unknown environmental dynamics. This paper addresses the challenge of controlling a drone as it traverses a swinging gate characterized by unknown dynamics. This paper introduces a parameterized MPC approach named hyMPC that leverages high-level decision variables to adapt to uncertain environmental conditions. To derive these decision variables, a novel policy search framework aimed at training a high-level Gaussian policy is presented. Subsequently, we harness the power of neural network policies, trained on data gathered through the repeated execution of the Gaussian policy, to provide real-time decision variables. The effectiveness of hyMPC is validated through numerical simulations, achieving a 100\% success rate in 20 drone flight tests traversing a swinging gate, demonstrating its capability to achieve safe and precise flight with limited prior knowledge of environmental dynamics.