Disrupted terrains that form as a consequence of giant impacts may help constrain the internal structures of planets, asteroids, comets and satellites. As shock waves and powerful seismic stress waves propagate through a body, they interact with the internal structure in ways that may leave a characteristic impression upon the surface. Variations in peak surface velocity and tensile stress, related to landform degradation and surface rupture, may be controlled by variations in core size, shape and density. Caloris Basin on Mercury and Imbrium Basin on the Moon have disturbed terrain at their antipodes, where focusing is most intense for an approximately symmetric spheroid. Although, the icy saturnian satellites Tethys, Mimas, and Rhea possess giant impact structures, it is not clear whether these structures have correlated disrupted terrains, antipodal or elsewhere. In anticipation of high-resolution imagery from Cassini, we investigate antipodal focusing during giant impacts using a 3D SPH impact model. We first investigate giant impacts into a fiducial 1000 km diameter icy satellite with a variety of core radii and compositions. We find that antipodal disruption depends more on core radius than on core density, suggesting that core geometry may express a surface signature in global impacts on partially differentiated targets. We model Tethys, Mimas, and Rhea according to their image-derived shapes (triaxial for Tethys and Mimas and spherical for Rhea), varying core radii and densities to give the proper bulk densities. Tethys shows greater antipodal values of peak surface velocity and peak surface tensile stress, indicating more surface damage, than either Mimas or Rhea. Results for antipodal and global fragmentation and terrain rupture are inconclusive, with the hydrocode itself producing global disruption at the limits of model resolution but with peak fracture stresses never exceeding the strength of laboratory ice.