We present the first simulations of tidal stirring of dwarf galaxies in the Local Group carried out in a fully cosmological context. We use the ErisDARK cosmological simulation of a Milky Way (MW)-sized galaxy to identify some of the most massive subhalos (Mvir > 108 M⊙) that fall into the main host before z = 2. Subhalos are replaced before infall with extremely high-resolution models of dwarf galaxies comprising a faint stellar disk embedded in a dark matter halo. The set of models contains cuspy halos as well as halos with “cored” profiles (with the cusp coefficient γ = 0.6) consistent with recent results of hydrodynamical simulations of dwarf galaxy formation. The simulations are then run to z = 0 with as many as 54 million particles and resolutions as small as ∼4 pc using the new parallel N-body code ChaNGa. The stellar components of all satellites are significantly affected by tidal stirring, losing stellar mass, and undergoing a morphological transformation toward a pressure supported spheroidal system. However, while some remnants with cuspy halos maintain significant rotational flattening and disk-like features, all the shallow halo models achieve vrot/σ⋆ < 0.5 and round shapes typical of dSph satellites of the MW and M31. Mass loss is also enhanced in the latter, and remnants can reach luminosities and velocity dispersions as low as those of ultra-faint dwarfs.