Ensuring high throughput and stable connectivity for mobile user equipment (UEs) with multiple receiver antenna panels is a key challenge in modern mobile networks. It is well-established that current handover mechanisms, based on procedures from the Third Generation Partnership Project (3GPP), exhibit performance limitations, especially in scenarios with high mobility at cell edges or at large distances from the base station (BS). In these areas, the strong influence of shadowing is known to cause an excessive number of unnecessary handovers (HOs), which significantly reduce throughput and reliability. To overcome this limitation, we introduce a novel framework based on Deep Q-Networks (DQN) to optimize handover decisions in Non-Coherent Joint Transmission (NCJT) mobile scenarios. Our approach enables the UE to control the selection of the transmission reception points (TRPs) autonomously and intelligently. We design and train the DQN for two different operating modes: one designed for maximum throughput and one for maximum reliability. The simulation results confirm that the DQN-based approach increases the overall performance compared to the 3GPP legacy procedures in critical scenarios by up to $\bm{60\%}$. These results establish deep reinforcement learning as a powerful tool for adaptive mobility management of multi-panel UEs and open up promising application possibilities for future wireless systems that require intelligent and context-sensitive TRP selection.