(...the Lebanese government on the other hand, probably with the support from the world community, will ... make sure that the use of weapons will be the monopoly of the state," said Ehud Barak)
Yeah, and attacking the Lebanese Army's outpost and laying siege to ALL of the Lebanese thus destroying the credibility of anybody remotely friendly to Israel will really help this matter./sarcasm off. While the Lebanese would love for Israel to destroy Hezbollah, they would take it slightly personal when at the same time Israel destroys the Lebanese economy with impunity. It's like having someone beat up someone who is bullied and telling him: Hey, I'll beat you up until you control that bully who is three times your size!
Sometimes there are no neat, easy solutions. This is about survival.
A sovereign government is legally responsible to control activities on it's territory. In fact, one of the signs of a sovereign government is the ability to control activities on their territory.