、。
Mother is struggling to make ends meet without running into the red.
Literal
Mother [topic-は], deficit [obj-を] not-put-out [without-ずに] living [obj-を] establish [to-のに] struggle-is-doing.
Three pieces worth calling out. (1) 赤字を出す ('put out red letters') means to run a deficit — accounting vocabulary that entered everyday language. (2) ~ずに is the written/formal equivalent of ~ないで: 'without doing X.' (3) のに苦労する ('have trouble ~ing') uses の as a nominalizer and に to mark the thing one struggles with. 暮らしを立てる is 'establish a living' = 'make a living.'