See
http://www.theboxotruth.com/docs/bot3.htm
Unless you are using very light shot a drywall over frame wall will not stop a shotgun blast.
Two possible options move the kid or brick the interior of his wall.
If you have access to a range that allows testing you may be able to see if just a brick facade would work or if you need real brick. A steel plate could be placed under the wall board as well.