  We present results from wide-field imaging of the resolved stellar
populations of the dwarf spheroidal galaxies Cassiopeia III (And XXXII) and
Perseus I (And XXXIII), 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+/-0.12 mag (839 (+48,-450) kpc, or 156 (+16,-13) kpc from M31)
for Cas III and 24.47+/-0.13 mag (738 (+48,-45) kpc, or 351 (+17,-16) 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 Lacerta I (And XXXI) from earlier work, and
search for substructure within the RGB star populations of Cas III, Per I, and
Lac I. We find an overdense region on the west side of Lac I at a significance
level of 2.5-3-sigma and a low-significance filament extending in the direction
of M31. In Cas III, we identify two modestly significant overdensities near the
center of the galaxy and another at two half-light radii. Per I shows no
evidence for substructure in its RGB star population, which may reflect this
galaxy's isolated nature.
