。
She had very high hopes for her children.
Literal
She [topic-は] children [target-に] very big hopes [object-を] was-pinning.
望みをかける ('to pin one's hopes on, place expectations on') is a fixed verbal collocation built around 望み ('hope, wish') + かける ('hang, apply, place'). The image is of literally 'hanging' one's hopes onto someone, like draping fabric over a frame. Combines smoothly with 大きな ('big, great') for 'high hopes.' The progressive ~ていた marks the hope-pinning as an ongoing past state — not a single moment of hope but an enduring parental investment.