Difficult Question. Complex Answer.
Nobody wishes to see their children end up in a situation like that. But if the crime is serious enough to warrant prison time, there are several things to consider. If the child is of legal age and solely responsible for their actions, then NOT assisting the authorities in apprehending the child could be construed as harboring a fugitive or obstruction of justice or the parent could even be viewed as an accomplice.
If the child is still under the care of the parent (IE: living at home, or a minor) then the parent could be held responsible for the child's actions thus, causing the parent to share in the punishment.
Disciplining a child is never an easy job regardless of the manner in which the discipline is meted out. Every individual needs to know that they are responsible for their actions and accept the consequences, good or bad.
As far as being a "traitor", I believe that not reporting the child for committing a crime, is doing more of an injustice to the child than turning them in. By "looking the other way" you are in fact sending a message that "it's okay" to do what they did. It is possible that a history of this may have contributed to the child's decision to commit the crime in the first place.
In fact, NOT reporting the child would make the parent a traitor to the child, a traitor to themselves and most certainly a traitor to the law. Imprisonment is a harsh punishment to hand a child over to, however, in Biblical times, under the Mosaic law, if a child committed a crime that incurred the punishment of death, the parents were required to execute the punishment by stoning their own children.
Thankfully, modern times are not as barbaric, but the underlying principle still applies: the parents are responsible for teaching their children right from wrong and, to a limited degree, responsible for the actions of the child.
So, in my humble opinion, reporting a child for committing a crime does not make the parent a traitor, no matter how difficult it may be to do so.