We must clarify the laws of telling a young child to do melacha, as many people make the mistake of thinking that a child is allowed to do anything on Shabbat, so they turn him into the ‘Shabbat Goy’.
One may not tell a young child to do melacha on Shabbat; neither melacha ruled by the Torah or by rabbinical ordinance. Although, a young child under the age of three who does melacha on his own, like turning on the light etc. does not have to be stopped. Some people try to prevent it for the sake of the sanctity of Shabbat, but from the age of three and up, he should be removed from doing forbidden melacha.
According to the Code of Jewish Law, only the father may stop him, but according to the ruling of the Mishna Brurah, everyone must stop him, if we’re dealing with a Torah prohibition.
It is absolutely forbidden to tell a child, even under the age of three to do melacha on Shabbat. This prohibition is imposed on any adult even if he is not the father.
Though, according to the letter of the law, one may place his child next to a light switch so he may turn the light on or off by himself, even though this is disrespectful to Shabbat as you are taking a child and making him commit a transgression on Shabbat. Therefore, it is not advisable to do so unless there’s a great need – for example, turning off the lights so that the children can fall asleep and so on.
Anytime a child does melacha on his own, the adult is allowed to benefit from it.