。
She was flustered by her children's behavior in front of others.
Literal
She [topic-は] children [genitive-の] in-front-of-people [genitive-の] manners [target-に] became-flustered.
うろたえる ('to be flustered, panic, lose composure') is a slightly literary verb capturing not just embarrassment but a flustered, scrambling response. 人前 ('in front of people, in public') is a culturally weighty noun in Japan: appearance and conduct in public bear special significance, captured in concepts like 世間体 ('appearance to society') and the strong inherited norm against 人に迷惑をかける ('causing trouble for others'). Children misbehaving 人前で is therefore not just embarrassing but socially fraught.