Over the past few years, the Internet-of-Underwater-Things (IoUT) became a prominent technology for investigating the underwater conditions. Moreover, the communication networks became heterogeneous over the past few years due to deployment of various technologies between the source and target nodes on the end-to-end (E2E) path. In heterogeneous IoUT networks, the nodes on an E2E path may consist of different traffic classes (TCs). Hence, the legacy model of networking and the default software-defined networking (SDN) will not be effective with inter-domain communication and E2E mapping of TCs. In this study, we propose a state-of-the art methodology utilizing SDN to fulfill the E2E service needs among domains with various TCs on the E2E path for the heterogeneous IoUT networks. We propose a module in the controller based upon a multi-criteria decision-making strategy i.e. simple additive weighting module (SAWM) to select a significant service class from the TCs. Moreover, we map the TCs in the global programmable controller (GPC) to meet an E2E quality-of-service (QoS) that meets application demands. Finally, we validate the supremacy of our proposed scheme through comparisons for E2E TCs mapping in terms of network performance metrics. The proof-of-concept experiments validate the effectiveness of the proposed strategy.