Supernova explosions within wind-driven bubbles are studied with 2D hydrodynamical calculations. Two different density distributions for the ejecta are considered: (1) a smooth, unfragmented power-law stratification, and (2) a fragmented distribution. As in 1D models, the presence of the shell of interstellar swept-up matter causes the rapid evolution of the remnant to the radiative phase. The main 2D effects, for both fragmented and unfragmented ejecta, include: (1) substantial chaotic deviations from a purely radial flow in the remnant interior, (2) efficient turbulent mixing between the ejecta and the shocked wind, resulting in homogenization of the former wind cavity, and (3) severe distortion of the wind-driven shell by cooling and Rayleigh-Taylor instabilities. In the case of the fragmented ejecta, additional important effects occur. These, which shape the resulting remnant, include: partial disruption of the shell by fragment impact, the generation of an outer rim of enhanced X-ray emission, and efficient mixing between interstellar, wind, and supernova matter. Explosions in wind cavities display a rich variety of features which may be useful in explaining why many Galactic supernova remnants appear to be in the Sedov phase rather than in the longer lasting radiative phases.