An intelligent transportation system (ITS) is a cyber physical system (CPS) that is well recognized due to its distinctive applications such as passenger safety, enhanced traffic efficiency, and infotainment services. However, very recently, these CPSs have witnessed a rapid increase in the number of autonomous vehicles (AVs), and the count is expected to increase significantly in the years to come. Under such scenarios, the conventional ITS solutions would fall short due to numerous technical limitations such as reduced flexibility, poor connectivity, limited scalability, and lack of adequate intelligence. In this direction, the cloud computing paradigm would also lag behind in meeting the following expected challenges: high mobility, minimal latency, realtime services, and high quality of service (QoS). Software defined networking (SDN) and edge computing (EC) are expected to be promising solutions for modern ITS. SDN allows efficient management of networks by virtue of its decoupled data and control planes. Moreover, EC is an extension of cloud computing that allows data processing, storage, and management at the edge of the network. Thus, these promising paradigms can address the network and data processing challenges of AV networks in rea time. Further, distributed mobility management (DMM) with improvised routing capabilities in the considered setup can bring added advantages in the form of zero tunneling overhead, full-fledged control of flow table entries, QoS-driven routing decisions, and efficient interplay between the edge and the cloud. Keeping in view the potential benefits of SDN, EC, and DMM in future AV networks, this work presents a composite framework with a distributed SDN-DMM approach in ITS ecosystems. Further, conventional DMM has been improved by stacking the Optimized Routing Decision module on it. This coupling yields a mobility-aware and QoS-driven (MobQoS) SDN framework for AVs that handles both the mobility and QoS challenges of the underlying vehicular networks. Additionally, it is also designed to handle the interplay between the edge and the cloud in an optimized manner using the Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D). Numerical comparisons depict that the proposed MobQoS outperforms the existing state of the art in terms of overall communication latency and bandwidth utilization. The performance assessment has been carried out using NS-3 and SUMO wherein an overall improvement of 15.95 percent has been reported in terms of end-to-end delay.