。
She finally made up her mind to separate from her husband.
Literal
She [topic-は] finally husband [with-と] separate-thing [object-を] decided.
とうとう carries a heavier emotional weight than the near-synonyms ついに or ようやく — it implies the outcome was long building, often regrettable or hard-earned. 決意する ('to make a firm resolve, to determine') is stronger than 決める ('decide') and stronger still than 思う ('think about'); it signals an inner commitment rather than a casual choice. 分かれる written as わかれる in kana works equally well, but the kanji 別れる would be the more usual choice for marital separation specifically. The sentence frames a heavy decision in deliberately weighty vocabulary.