No way are the South Koreans keeping the nukes. Obama, with the new anti-nuclear rhetoric and debates over proliferation in Iran, won't be happy with it. Japan won't be happy with it due to the animosity with Korea and the anti-nuclear sentiment. And China sure as hell will be pissed about it, considering that they will share a land border with a new nuclear power, upsetting the status quo.
If this happens after Obama we might well let them keep the nukes depending on what relations with China are like. Dangerous yes but if unification occurs after some Taiwan Straits crisis or similar US-PRC issue, the US might like the idea of a nuclear ally in the region a la France and Britain in the Cold War.