。
Don't treat me like a kid.
Literal
Me [object-を] child-treatment do-[don't-な]-[insistence-よ].
扱い ('treatment, handling') is the noun form of 扱う ('to handle, treat'). 子供扱い ('treating like a child') is a productive compound — [noun]扱い means 'treating as [noun].' Other examples: 客扱い ('treating as a customer'), 物扱い ('treating as an object'). The prohibitive ~な + insistence よ makes this a firm protest.