Electron cooling together with intra-beam scattering results in a transverse distribution that can best be described by a sum of two gaussians, one for the high-density core and one for the tails of the distribution [1]. Simulation studies are being performed to understand the beam-beam interaction of these double-gaussian beams. Here we report the effect of low-frequency random tune modulations on diffusion in double-gaussian beams and compare the effects to those in beam-beam interactions with regular gaussian beams and identical tune shift parameters.