My mother does her shopping on the way home from work.

Literal

Mother [topic-は] work [possessive-の] return [at-に] shopping [object-を] does-[polite-ます]

勤めの帰りに = 'on the way back from work.' 勤め (つとめ) = employment/job. 帰り = the return/way home. に marks the timing.