、。
Since mother had fallen sick, we sent for a doctor.
Literal
Mother [subject-が] illness [became-になった] [because-ので], we [topic-は] doctor [obj-を] call [purposive-に] sent.
Two patterns to notice. (1) 病気になる is the fixed 'become sick' — な-adjective/noun + になる. (2) 呼びにやる uses the purposive ~に (stem of a verb + に = 'in order to') with やる meaning 'send' or 'dispatch.' The full idiom 医者を呼びにやる is 'send someone to call a doctor' = 'send for a doctor.' ので is a softer 'because' than から, often feeling more objective or factual.