。
She's looking forward to her son's future with great anticipation.
Literal
She [topic-は] son [genitive-の] future [object-を] greatly looking-forward-adverbial is-doing.
楽しみにする ('to look forward to') is the set frame combining the noun 楽しみ ('enjoyment, anticipation') with adverbial に + する ('do'). It's productive for anything anticipated — events, meals, meetings, futures. 大いに ('greatly, very much') is a formal/written intensifier modifying the action of looking forward. ~にしている marks ongoing anticipation: 'is in the state of looking forward.'