My mother is afraid of causing an accident and never drives.
Literal
Mother [topic-は] accident [object-を] cause thing [object-を] fearing-[sequential-て], absolutely car [object-を] drive-not-[polite-ません]
事故を起こすことを恐れて = 'fearing the act of causing an accident' — こと nominalizes, 恐れる = to fear. 決して~ません = 'absolutely never' — 決して requires a negative verb. The causal て links the fear to the habitual avoidance.