Mother [possessive-の] face [on-に] despair [possessive-の] color [subject-が] vividly was-visible
ありありと = vividly/plainly — a mimetic-style adverb for something unmistakably clear. 絶望の色 = 'the color of despair' — 色 (color) used metaphorically for an emotional expression on someone's face, a literary Japanese convention.