Integration of trajectory optimization into sequence optimization is required for next-generation Arrival Managers (AMANs) to support Collaborative Decision-Making (CDM) and implementation of user-preferred 4D trajectories. In addition, considering uncertainty in the optimization is also necessary for making more robust decisions. To achieve these aims, this study proposes a method to integrate the trajectory and sequence of approach aircraft in a single optimization framework and calculate optimal robust solutions against weather forecast uncertainty. This uncertainty is quantified utilizing the ensemble weather forecast and the robust optimizations for trajectory and sequence are formulated in an ensemble approach. To connect the two optimizations, we introduce the so-called performance surfaces, which represent the characteristics of the optimal trajectory. The resulting integrated Trajectory and Sequence (T&S) optimization is a combination of the robust Optimal Control (OC) and Mixed-Integer Nonlinear Programming (MINLP). The MINLP problem is relaxed to the corresponding Nonlinear Programming (NLP) problem to reduce computational costs. In the case study, the trajectory and sequence are simultaneously optimized for two different objectives: the maximum throughput at the merging point and the minimum fuel burn while maintaining the inter-aircraft separation.