It might be cool to be able to send your young children to another country for a time. Might be cool if you fall in relation to another country they then use your child as a bargaining chip. In medieval times kings would often keep children of other lords under their "protective" care to ensure the loyalty of other lords and such. The same could happen with other kings sons and daughters as well.
This is a good idea. George RR Martin writes about this in the Game of Thrones - where children of a conquered noble are sent to "stay" with the victor - to ensure the conquered's loyalty. Or,alternatively, where the children of the conqueror are sent to stay with the vanquished noble - perhaps as a sign of trust in the defeated noble. This could be a fairly interesting game mechanic. It would be interesting to use offspring as trip wires; like troops stationed in foreign countries as a deterrent to common enemies to show allies' resolve to act together.
Yep, using children as bargaining chips, adoptive wards, loyalty ensurers ... or even to raise the son of a MORTAL lord (of a Minor Nation) as your squire/apprentice/Lancer in order to win the trust/allegiance of that Minor nation, or even to gain control over its resources once the son takes the throne.
Basically, even out-side of marriage there are plenty of ways to use children in diplomacy. Heck, maybe if you have another lord's child in your court it would increase the chances of that child marrying/ seeking marriage with a child of your own. (at least a child of your own that is also in your court)
I am reminded of Attila the Hun growing up in a Roman City, with Roman teachers and luxuries ... being close friends with a Roman child that grew up to be a Roman general. And the eventual battle vs Attila and his childhood friend many years later.
IIRC both children spent some of their childhood in the Realm of the Huns and some of their childhood in the Palaces of Rome.