[When] may a koton be asked to turn on hot water on Shabbos?
One is not allowed to tell a minor to do a malochoh deorysah on Shabbos even if the child has not reached the age of chinuch. Regarding a melochoh derabonon is a dispute amongst the Rishonim and the Chofetz Chaim is mekel if it is for the child’s benifit. The are those who permit to tell a minor to do a malocho derabonon if it is necessary for a mitzvoh. It is preferable that someone else and not the father tell the child to do the issur derabonon.
O:CH 443 Biur Halachah ד”ה מד”ס Shulchan Aruch Harav 443:6