。
She was deeply embarrassed because her child misbehaved in public.
Literal
She [topic-は] child [subject-が] in-front-of-people [at-で] manners-ill was [because-ので] very was-flustered.
A culturally rich sentence about 人前で行儀悪い — misbehaving in public. 行儀 ('manners, etiquette, conduct') is heavily socially weighted in Japanese parenting; 行儀よく しなさい ('behave properly') is one of the most common parental directives. お行儀 with the polite prefix お adds a slight formality or feminine flavor. 当惑する ('be perplexed, embarrassed, at a loss') describes a flustered, internally-disrupted feeling — heavier than 困る ('be troubled') and overlapping with embarrassment. ので is the soft 'because' (vs. blunter から).