The child ticketed in another cabin isn't going to work, unless there's an "adult" in the child-accompanying ticketed cabin.
Also, the airline crew will rather easily know whether or not a given ticketed-and-seated passenger has a lap-child allowance or not. The lap-child thing is going to be a very hard sell when dealing with a 3 year-old on an international flight.
Note that some airlines do provide child discounts for international tickets, even sometimes for business class seats.