。
She just didn't want to go out, no matter what.
Literal
She [topic-は] anyway out-go-want-not-was.
とにかく ('anyway / in any case / regardless') is a hedge that often signals 'leaving the reasons aside' — here amplifying her reluctance by waving away whatever rationale anyone might offer. 外出する pairs 外 (outside) with 出 (exit) into a Sino-Japanese compound that feels more deliberate or formal than the everyday 出かける.