Does sound a little tough for you. According to you, the waters around the island are in dispute, which gave the North the justification they needed to sink the South's boat, and any further South presence in this area is more justification for "response" from the North? If a valid argument, wouldn't just the very presence of South citizens on this island represent a provocation to the North? Would the South be justified in patrolling this area to protect its citizens from Northern attack or do you see this patrolling as further provocation as the South has no legal grounds on which to stand in order to protect its citizens on this island?
Sending naval forces into a disputed area is a provocation, see China’s reaction if Japan did that with the island in the South China Sea or when America trys to sends a carrier into the Yellow Sea.
The whole thing is tit for tat and not approved by the South Korean people - it will die down in a couple of days even if the hysteria continues in other parts of the world.