Considering the increasing emphasis on sustainable development, global warming effects have received attention for properly managing enterprise activities such as manufacturing, energy utilisation, resource consumption, and carbon emissions. The effect of greenhouse gases generated by carbon emissions is the most significant. This study develops a dual-channel supply chain system that consists of duopoly manufacturers and two common retailers and investigates the effects of the pricing policy, the decision-maker’s mental accounting, and carbon emission reduction investments on the channel members’ decisions. We conduct a numerical experiment, demonstrating that investments in carbon emissions reduction decrease carbon emissions while enhancing market competitiveness and profitability. This is primarily because customers prefer green products and exhibit higher brand loyalty, which makes them willing to pay premium prices for environmentally friendly products. Additionally, the leader-follower model shows the dominant role of leaders in pricing and investment decisions, while the multichannel structure highlights the importance of channel synergy. This study contributes to the field by examining intra- and inter-channel competition issues among leader-follower channel members within a multi-channel structure. This analysis facilitates practical profit-maximisation decision-making.