。
She loudly scolded her son for staying out late.
Literal
She [topic-は] son [subject-が] late [until-まで] wandered-about [quotative-と] saying loud-voice [with-で] scolded.
出歩く ('go out and wander, be out and about') is a compound 出る + 歩く ('exit + walk') for being out of the house, especially during late or improper hours. The ~と言って ('saying that X') frame here means 'on the grounds that' or 'with the rebuke that' — common with verbs of scolding, complaining, or commenting. The whole gives 'scolded, saying X.' 大声で叱る ('scold loudly') is a natural collocation; 叱る is the everyday parental scolding verb.