。
She wished for her son's success.
Literal
She [topic-は] son [genitive-の] success [object-を] hoped-for.
望む ('to hope for, desire, wish for') is a clean, standard verb for hoping or wanting. Takes the desired outcome with を. Note that English 'wish for' often demands specific verbs depending on the type of wish (long for, dream of, hope for); Japanese 望む covers most of these. The past 望んだ ('hoped for') here narrates a completed wish or one held over a period.