。
She takes pride in her sons' success.
Literal
She [topic-は] sons [genitive-の] success [object-を] pride [adverbial-に] is-doing.
Xを誇りにする ('take pride in X') uses the productive ~にする ('make into') frame, treating the prideful object as something turned into a source of pride. Plurality matters here — the plural marker 息子たち pluralizes 息子 ('son'), so the speaker has multiple sons whose collective success is a source of pride. ~ている marks the ongoing pride state.