During the cold war, the US and the USSR should have had an informal arrangement where the president's daughters go study in Russian universities, and the premier's kids come to DC. Their life wouldn't have to be bad there - both cities have expat populations, and fun stuff to do.
It would have made it very unlikely that the US would have launched an unprovoked attack. Think how much more comfortable it would be to live in Moscow if Reagan's daughter was known to be living there.
They would need to be monitored, to make sure they didn't just run away, but that could be done discreetly. They wouldn't even all need to be monitored at all times - only half of them for example would need to be secure at any one time. The rest could just go run wild.
The people living overseas might fall in love locally or make other friends, and end up being suspected of being double agents.