Mothers should not let their children play in the road.
Literal
Mothers [topic-は] children [to-に] road [at-で] play-[causative-させ]-not [goal-ようにする] should-[べきだ]
Deeply layered: 遊ばせない (negative causative = not let play) + ようにする (make it so that) + べきだ (should). The whole chain = 'should make it so that they don't let (children) play.' Three grammar layers stacked.