。
She had been counting on his promise.
Literal
She [topic-は] his [genitive-の] promise [object-を] hope [to-に] doing was.
当てにする (or 当てにしている) is a set phrase meaning 'to count on, rely on, bank on' — 当て ('aim, hope, expectation') + にする ('make X into') = 'make (it) into one's expectation.' The を marks what's being relied on, the に+する frame conveys 'set as a basis for one's plans.' The past continuous ~ていた often implies the reliance later turned out misplaced — 'had been counting on (and now perhaps regrets it).'