If I understand correctly the waters that are currently occupied by the south are disputed. The south alledgedly was lobbing shells into the waters north of the disputed territory (ie into undisputed waters).
I'm not favouring any claims, just putting out the facts to the angry mob 
I dont know about that. First off: Possesion of any disputed territory is 9/10ths ownership.
Also, Facts are the leading cause of deception in most cases.
If the North wants to take the South to war over this dispute I do not see what choice the South has other than full out war or capitulation.
A single tactical nuclear weapon detonated in Pyongyang should end it decisively, before millions die all across the peninsula in a drawn out war.