。
She had no choice but to go alone.
Literal
[topic-は] cannot-be-helped one-person [with-で] went.
やむえず is a colloquial dropped-を rendering of やむを得ず (the standard form). In careful writing, the standard form with を is preferred. 一人で ('alone, by oneself') uses the instrumental で to mark the manner of going — 'in a state of being one person.' This 一人で usage is among the most common applications of で for marking manner.