。
She could tell at a glance that her daughter had been crying.
Literal
She [topic-は] at-one-look daughter [subject-が] was-crying [quotative-と] understood.
一目で ('at a glance / at first sight') is an adverbial 'one-look' marker — 一 ('one') + 目 ('eye') + で. It precedes verbs of perception or recognition: 一目でわかる ('understand at a glance'), 一目で気に入る ('like at first sight'). The embedded clause 娘が泣いていた is wrapped by と and the verb わかる ('know, recognize, realize') — note that the が in the embedded clause (rather than は) is mandatory in subordinate clauses; topic-marker は is restricted to matrix clauses. ~ていた as past progressive captures 'had been crying.'