。
She got her way.
Literal
She [topic-は] her own claim [object-を] pushed-through.
通す ('to pass, push through') with 主張 as object is a fixed collocation: 主張を通す ('to push one's claim through, to get one's way, to have one's argument prevail'). The verb 通す is rich — its core sense is 'to make something pass through/along' — and it pairs with various objects to give different idiomatic readings: 目を通す ('skim'), 意地を通す ('stick to one's principles'), 独身を通す ('remain single'). Here it gives the satisfying image of forcing one's view through opposition.