<p>This study investigates a two-dimensional dynamical system with double discontinuity and a frequency-switching periodic force. The discontinuity surfaces partition the phase space into three regions. Using the Filippov convex method, geometric singular perturbation theory, and blow-up analysis, the existence and boundaries of sliding regions are established and the stability of the sliding dynamics is characterised. The analysis reveals that frequency switching can generate repelling sliding modes on the switching surfaces, in contrast to cases commonly reported in the literature. A cylindrical blow-up framework is developed to analyse the codimension-2 discontinuity at the intersection of switching surfaces, providing deeper insight into the local dynamics. The theoretical results are applied to a predator–prey model featuring a double-threshold control strategy and periodic environmental fluctuations in the prey population, and the analysis is validated through numerical simulations. Discontinuity-induced bifurcations (DIBs) are explored numerically, uncovering a novel phenomenon in which distant DIBs occur simultaneously at different switching surfaces. Bifurcation diagrams for key parameters reveal rich and complex dynamics, including period-adding cascades arising from grazing bifurcations, period-doubling and period-halving bifurcations, and chaotic behaviour. Multistability is also observed, indicating strong sensitivity to initial prey and predator densities.</p>