The moment the child saw mother, he cheered right up.

Literal

Mother [gen-の] figure [obj-を] see and child [topic-は] immediately well [became-になった].

姿 is 'figure,' 'appearance,' or 'the sight (of someone)' — often used when describing someone appearing visually. 元気になる is the standard 'cheer up' / 'get better,' with に marking the result state and なる ('become') as the verb. The て-form of 見る chains the seeing to the cheering-up as a cause-effect sequence.