。
She's good at handling kids.
Literal
She [topic-は] child [genitive-の] handling [subject-が] is-skillful.
A tighter rephrasing of 'good with children': 扱い is the noun form of 扱う, and うまい takes it as a が-marked subject. The bigger pattern is the [noun] が うまい / 上手 frame for skill at a thing — 料理がうまい ('good at cooking'), 歌がうまい ('good at singing'). Compare with the verb-based [verb dictionary]+のがうまい frame for skill at an action; the noun form is shorter and snappier when a noun is available.