Are there historical examples of a noble or other representative of a nation-state exchanging his own child or other children from his nation-state with those of an enemy, in order to solidify a friendship or peace treaty between those nations?
The Romans would accept and raise the highborn of allied tribes, hoping to Romanize their future leaders and cement their political and military relationships. Maroboduus was a ward of Augustus. Later, as king of the Marcomanni, he organized a confederation of tribes to defend against Rome.
This was also the case with the Germanic Cherusci tribe, which was for some time considered an ally of Rome. The Cheruscan chieftain Arminius was raised in Rome, though it seems difficult to tell from the record exactly what his status was (hostage? ward?). In any case, Arminius was introduced to Roman culture and military practices. He received citizenship and command of auxiliary forces that fought for Rome. He seemed Romanized enough that he was trusted by the general Publius Quinctilius Varus on an expedition into Germania. This was a mistake, albeit a very quotable mistake.