To increase the redundancy and to provide seamless connectivity of the conventional communication systems, an unmanned aerial vehicle (UAV) enabled on-demand forwarding base station approach can be a flexible and dynamic solution, particularly for emergency services. However, managing and controlling these UAVs in changing scenarios can be challenging specifically in large-scale network scenarios. As a promising method of administering these networks, software-defined networking (SDN) can be a good choice compared to traditional networking due to its automated, centralized, and intellectual controllability. Therefore, to meet the future sixth-generation wireless communication requirements with high network availability, improved communication convergence, and intelligent features, a software-defined UAV (SDUAV) networking framework is proposed in this work. To enhance the reliability and scalability, and to reduce the single-point failure issues of this network, a multi-SDN controller-based approach is also deployed in this newly designed architecture. Besides, to solve the load balancing and fault tolerance problems like controller overhead or cascading failure, an adaptive load balancing algorithm as well as a robust hybrid routing algorithm are developed, accordingly. In addition, to evaluate the performance of the proposed architecture, a mathematical model is proposed by using the M/M/1 and M/M/c queueing systems at the primary and secondary controllers, respectively. Simulation results show that the proposed model reduces the packet processing time by 60%, 44%, and 25% in terms of packet arrival rate, service rate, and utilization factor, respectively, compared to the existing control-domain adjustment algorithm.