We present results from wide-field imaging of the resolved stellar populations of the dwarf spheroidal galaxies CassiopeiaIII (AndXXXII) and PerseusI (AndXXXIII), two satellites in the outer stellar halo of the Andromeda galaxy (M31). Our WIYN pODI photometry traces the red giant star population in each galaxy to ~2.5-3 half-light radii from the galaxy center. We use the tip of the red giant branch (TRGB) method to derive distances of (m-M)0=24.62{+/-}0.12mag (839_-45_^+48^kpc, or 156_-13_^+16^kpc from M31) for CasIII and 24.47{+/-}0.13mag (738_-45_^+48^kpc, or 351_-16_^+17^kpc from M31) for Per I. These values are consistent within the errors with TRGB distances derived from a deeper Hubble Space Telescope study of the galaxies inner regions. For each galaxy, we derive structural parameters, total magnitude, and central surface brightness. We also place upper limits on the ratio of neutral hydrogen gas mass to optical luminosity, confirming the gas-poor nature of both galaxies. We combine our data set with corresponding data for the M31 satellite galaxy LacertaI (AndXXXI) from earlier work and search for substructure within the RGB star populations of CasIII, PerI, and Lac I. We find an overdense region on the west side of Lac I at a significance level of 2.5{sigma}-3{sigma} and a low-significance filament extending in the direction of M31. In CasIII, we identify two modestly significant overdensities near the center of the galaxy and another at two half-light radii. PerI shows no evidence for substructure in its RGB star population, which may reflect this galaxy's isolated nature.