。
She kept the secret from her husband her entire life.
Literal
She [topic-は] whole-life that secret [object-を] husband [from-に] kept-hidden.
~ておく on 隠す reads as 'hide and leave it that way' — the auxiliary おく ('place, set down') signals deliberate maintenance of a state. Unlike one-off 隠した ('hid'), 隠しておいた suggests sustained concealment over time, which fits the 一生 ('whole life') frame. に here marks the person from whom information is withheld — Japanese particle direction is opposite of English: hiding from someone is ~に隠す.