We investigate the dynamics of dual disease epidemics within the spatial rock-paper-scissors model. In this framework, individuals from all species are equally susceptible to infection by two distinct pathogens transmitted via person-to-person contact. We assume antagonistic mortality, where the simultaneous occurrence of coinfection reduces the probability of host mortality due to complications arising from either coexisting disease. Specifically, we explore two scenarios: global antagonism, where the presence of one pathogen inhibits the progression of the other in coinfected hosts, and uneven antagonism, where only one pathogen affects the development of the other. Using stochastic simulations, we show that the characteristic length scale of the spatial patterns emerging from random initial conditions diminishes as antagonism becomes more significant. We find that antagonism enhances species population growth and reduces the average probability of healthy organisms becoming infected. Additionally, introducing individuals' mobility restrictions significantly decreases both organisms' infection risk and selection pressures. Our results demonstrate that combining mobility restrictions with antagonistic coinfection can increase organisms' life expectancy by up to $54\%$. Our findings show that integrating antagonistic coinfection and mobility restriction strategies into ecological models may provide insights into designing interventions for managing concurrent epidemics in complex systems.