The performance of Cu-exchanged chabazite (Cu-CHA) for the ammonia-assisted selective catalytic reduction of NOx (NH3-SCR) depends critically on the presence of paired \({[{{{\rm{Cu}}}}{({{{{\rm{NH}}}}}_{3})}_{2}]}^{+}\) complexes. Here, a machine-learning force field augmented with long-range Coulomb interactions is developed to investigate the effect of Al-distribution and Cu-loading on the mobility and pairing of \({[{{{\rm{Cu}}}}{({{{{\rm{NH}}}}}_{3})}_{2}]}^{+}\) complexes. Performing unbiased and constrained molecular dynamics simulations, we obtain unique information inaccessible to first-principle calculations and experiments. The free energy barrier for \({[{{{\rm{Cu}}}}{({{{{\rm{NH}}}}}_{3})}_{2}]}^{+}\) diffusion between CHA-cages depends sensitively on both the local and distant Al-distribution. Importantly, certain Al-distributions and arrangements of neighboring \({[{{{\rm{Cu}}}}{({{{{\rm{NH}}}}}_{3})}_{2}]}^{+}\) and \({{{{{\rm{NH}}}}}_{4}}^{+}\) cations make paired \({[{{{\rm{Cu}}}}{({{{{\rm{NH}}}}}_{3})}_{2}]}^{+}\) complexes exothermic with respect to separated configurations. Our results suggest that the NH3-SCR activity can be enhanced by increasing the Cu-loading and Al-content. The dynamic interplay between \({[{{{\rm{Cu}}}}{({{{{\rm{NH}}}}}_{3})}_{2}]}^{+}\) and \({{{{{\rm{NH}}}}}_{4}}^{+}\) diffusion is crucial for the \({[{{{\rm{Cu}}}}{({{{{\rm{NH}}}}}_{3})}_{2}]}^{+}\) mobility and stresses the need to explore large systems including long-range Coulomb interactions when studying diffusion of charged species in zeolites.