A sibling exchange. 掃除しといて is the colloquial contraction of 掃除しておいて (the ~ておく 'do in preparation' form + ~てください implied). アゴで使う literally 'to use someone with one's chin' is a set idiom meaning 'to order someone around imperiously, treat someone like a servant' — evoking the image of someone lazily directing others with a jerk of the chin. ~なよ is a soft prohibitive.