The Lebanese government is basically a joke. The Lebanese military is little better. The international peacekeeping force has never done anything meaningful to separate Hezbollah from the Israelis. As a result, you can certainly understand why the Israeli government has shown minimal interest in an international solution to the Hezbollah problem.
But what are the better alternatives? Israel’s attempt to create a proxy force in the border areas was a failure and would be no more successful today. That leaves two options: an indefinite occupation at a time when the country’s resources are already being stretched in Gaza; or a withdrawal after a short period of time that results in Hezbollah, weakened but not destroyed, returning to the border area with thousands of rockets and the will to use them.
In short, if the objective of the Hezbollah campaign is to provide permanent security for the residents of Israel, it will almost certainly fail. The Israelis are much better at tactics than they are at strategy.