Mobile robots are nowadays frequently used for interaction tasks in the real world, e.g. for opening doors or for pick-and-place tasks. When used in real-world environments, adapting the robot controllers to uncertain contact dynamics is a significant challenge. Adaptive Model Predictive Control (AMPC) is an approach for controlling robot motions while adapting to uncertain or changing dynamics. However, most of the existing AMPC approaches used in mobile manipulation require either expert tuning or extensive training, making it very difficult to introduce novel or diverse tasks. In addition, the adjustment of several, independent environment parameters is usually not considered in the AMPC formulation. In this work, we introduce a hierarchical approach that uses Gaussian Mixture Models (GMMs) and Gaussian Mixture Regression (GMR) to predict the dynamic model parameters of MPC based on proprioceptive measurements and perform tasks with multiple unknown environmental parameters. The approach is evaluated in simulation and in real experiments on a mobile manipulator and compared to several baseline methods. It is shown that it outperforms standard MPC and an existing AMPC approach on several tasks such as carrying, pushing, and door opening.