Integrated Demand Response (IDR) as a crucial method for maintaining supply-demand balance and realizing the local consumption of distributed energy in Regional Integrated Energy System (RIES), has become a hot research topic. However, existing studies on IDR have two main shortcomings: they fail to consider the coupling relationship between response power and carbon emission quota in complex scenarios during regional transactions; and when customizing incentive strategies for consumers within regions, they overlook the fatigue characteristics of consumers. Therefore, this paper establishes an inter-regional coupled transaction mechanism of response power-carbon emission quota under complex scenarios. The incorporation of a response fatigue function enables the proficient representation of consumer response fatigue characteristics. Additionally, this paper proposes an adaptive iterative step size-based bargaining method to determine the optimal transaction price. The effectiveness of the proposed model is verified by simulation results: it not only reduces the total costs and carbon emission of IESP but also improves consumer benefits. The proposed bargaining method enhances bargaining efficiency.