A patterned mesoscale ferromagnetic disk in equilibrium can attain a flux closure vortex state with circumferential in-plane magnetization and an out-of-plane magnetic component (vortex core) at the center. When driven by a small-amplitude oscillating magnetic field or current, the vortex core gyrates around its equilibrium position experiencing resonance at a characteristic eigenfrequency. Here, we propose a resonant-spin-ordering approach for manipulating the relative vortex core polarities in coupled double-dot structures. This is achieved by driving the system to a chaotic regime of continuous core reversals and subsequently relaxing the cores to steady state motion. Any particular core polarity combination (and therefore the spectral response of the entire system) can be deterministically pre-selected by simply tuning the excitation frequency.