A Castle Doctrine (also known as a Castle Law or a Defense of Habitation Law) is an American legal concept arising from English Common Law that designates one's place of residence (or, in some states, any place legally occupied, such as one's car or place of work) as a place in which one enjoys protection from illegal trespassing and violent attack. It then goes on to give a person the legal right to use deadly force to defend that place (his/her "castle"), and/or any other innocent persons legally inside it, from violent attack or an intrusion which may lead to violent attack. In a legal context, therefore, use of deadly force which actually results in death may be defended as justifiable homicide under the Castle Doctrine.
Your home state is one such state that has a Castle Law. Is shooting a guy any less barbaric than letting him bleed for the same reason?
Here's a less barbaric solution for children at the border... let a cop car, stocked with water bottles, drive the child back to his home IN MEXICO.