Models are developed for the motion of charge-2 Abelian Higgs vortices through the 2-vortex moduli space , with the vortices excited by their shape mode oscillations. The models simplify to the wellknown geodesic flow on , modified by a potential, when the mode oscillations are fast relative to the moduli space motion and their amplitudes are small. When the lowest-frequency mode is excited with a large amplitude, the geodesic flow is not a correct description. Instead, a chaotic, or even fractal, multibounce structure in vortex-vortex collisions is predicted.