"I have to go out now but I will find and send you the biblical reference when I get back."
I am presuming you are refering to Deuteronmy 21: 18-21.
"If a man have a stubborn and rebellious son, which will not obey the voice of his father, or the voice of his mother ... all the men of the city shall stone him with stones, that he die."
There are two problems with your interpretation.
First, the person in view is a not a small child but a grown son or daughter.
It applies only when the parents have tried to restrain their son, but all their efforts have failed (vv. 18, 20); specifying that he is physically beyond their control. Furthermore, the parents bring their son to the magistrates to judge the matter (v. 19); hence, the son would have opportunity to speak on his own behalf.
In short, The law is not talking about naughty children but about seriously delinquent young adults.
Second, the problems associated with this son are severe. This is not the case of a child who has failed to do his chores, spoke back to his parents, or even committed a serious act of disobedience, but of a son of dissolute character who is in full rebellion to the authority of his parent--she holds them and their word in contempt. Thetext says that the son is "stubborn" and "rebellious" (vv. 18, 20).
Both of these descriptive terms are active participles, thus indicating habitual action. The son does not display a stubborn streak now and then, or act rebelliously from time to time, but is continuously stubborn and rebellious.
The word "stubborn" is a bit of a mis-translation. In the original Hebrew, it refers to one who is obstinate in his resistance to authority.
It is used in the Old Testament of a wild, untamed heifer (Hos. 4:16); of a immoral woman who has cast off restraint and indulges in lust (Pr. 7:11); and of Israel as a stubborn people who will not submit to God's authority (Ps. 78:8; Is. 1:23).
Similarly, the word "rebellious" means, literally, to strike or lash, and is used of those who contend against authority and refuse to heed their words. The "rebellious" individual lashes out in contempt against those who have authority over him verbally and physically.
So, what does the Law REALLY say?
In the case of such rebellion and riotous living, and after all attempts at discipline and control have failed, the parents are to bring their son before the magistrates for judgment. If the magistrates concur in the parents' estimate of the situation, they are to order the men of the city to stone the rebel with stones so that he dies (vv. 20-21).