Did I make a mistake, from a religious perspective, by accepting the price of the stolen goods that were not recovered from the juvenile thief, after he was caught red-handed with some of them?

The presence of some stolen items with the child does not necessarily mean that he stole the rest, and you cannot compel him to pay their price unless the amount paid was a settlement in exchange for not filing a lawsuit against his son. In this case, a settlement is permissible, for the Prophet, peace and blessings be upon him, said: "Settlement is permissible among Muslims, except for a settlement that forbids what is lawful or permits what is unlawful." Also, a settlement based on denial is permissible for bringing about benefits and averting harms. If the guardian donates the money of his own accord, there is no harm in you taking it, whether it is a settlement or a donation.