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Modern multi-access 5G+ networks provide mobile terminals with additional capacity, improving network stability and performance. However, in highly mobile environments such as vehicular networks, supporting multi-access connectivity remains challenging. The rapid fluctuations of wireless link quality often outpace the responsiveness of existing multipath schedulers and transport-layer protocols. This paper addresses this challenge by integrating Transformer-based path state forecasting with a new multipath splitting scheduler called Deep Adaptive Rate Allocation (DARA). The proposed scheduler employs a deep reinforcement learning engine to dynamically compute optimal congestion window fractions on available paths, determining data allocation among them. A six-component normalised reward function with weight-mediated conflict resolution drives a DQN policy that eliminates the observation-reaction lag inherent in reactive schedulers. Performance evaluation uses a Mininet-based Multipath Datagram Congestion Control Protocol testbed with traces from mobile users in vehicular environments. Experimental results demonstrate that DARA achieves better file transfer time reductions compared to learning-based schedulers under moderate-volatility traces. For buffered video streaming, resolution improvements are maintained across all tested conditions. Under controlled burst scenarios with sub-second buffer constraints, DARA achieves substantial rebuffering improvements whilst state-of-the-art schedulers exhibit near-continuous stalling.