What is the ruling on the money given by the father to his youngest son to trade with, this money being from the wealth of his siblings working abroad, so as to make him wealthy and employed like them?

If the children send money to their father as a gift, it becomes the father's property to dispose of as he wishes. However, if it is by way of agency for him to preserve or invest for them, he is not permitted to dispose of it except according to the terms of the agency.

If the father gifts money to one of his children, excluding their siblings, due to that child's poverty and need, this is permissible and there is no sin in it. The money becomes the son's property without any obligation to return anything to his siblings.