I like the concept of the game, of modifying the stage instead of the instructions itself, though I feel the puzzle ideas aren't as explored as they could've been. As others pointed out, a button to skip the timer would be really helpful, and maybe even just doing away with the timer entirely and just one button to start the level would work too.
Bug - when dragging around the moveable platforms, you can "push" the child around. You could use that to move him off screen, or even transport him to mom even before 30 seconds is up.
I like the mood though, it's pretty funny with the really scared child and the scary mom