Obviously Hezbollah started this and Hezbollah is the main problem. Not only did they drag my second home into a war, the bastards also threatened me personally. So I hardly see the point in telling you what I think about them right about now. I'll get to them later.
I sympathize one hundred percent with what Israel is trying to do here. But they aren't going about it the right way, and they're punishing far too many of the wrong people. Lord knows I could be wrong, and the situation is rapidly changing, but at this particular moment it looks bad for Israel, bad for Lebanon, bad for the United States, good for Syria, and good for Iran.
There is no alternate universe where the Lebanese government could have disarmed an Iranian-trained terrorist/guerilla militia that even the Israelis could not defeat in years of grinding war. There is no alternate universe where it was in Lebanon's interest to restart the civil war on Israel's behalf, to burn down their country all over again right at the moment where they finally had hope after 30 years of convulsive conflict and Baath Party overlordship.
The Lebanese government should have asked for more help from the international community. The Lebanese government should have been far less reactionary in its attitude toward the Israelis. They made more mistakes than just two, but I'd say these are the principal ones.
What should the Israelis have done instead? They should have treated Hezbollahland as a country, which it basically is, and attacked it. They should have treated Lebanon as a separate country, which it basically is, and left it alone. Mainstream Lebanese have no problem when Israel hammers Hezbollah in its little enclave. Somebody has to do it, and it cannot be them. If you want to embolden Lebanese to work with Israelis against Hezbollah, or at least move in to Hezbollah's bombed out positions, don't attack all of Lebanon.
The problem, from the Israeli perspective, is that you can't just divide Hezbollahland from the rest of Lebanon, if for no other reason than that the rest of Lebanon has resupply routes for Hezbollah (additionally, Hezbollah has offices and militants all throughout Lebanon, including Beirut). Ideally, you work with the Lebanese government to isolate and eliminate Hezbollah together. The problem with that is that Israel and Lebanon don't have diplomatic ties, and Israel doesn't trust Lebanon to uphold its end of the bargain anyway, as it already has been breaching its obligation under UN Resolution 1559 to conduct the disarming process. What Israel is banking on is that its bombing runs will a) convince Lebanon that harboring Hezbollah is more trouble than it's worth and b) weaken Hezbollah so that Lebanon can actually act on the new-found revelation triggered by "a". It's possible that will happen. It's also possible that the Israeli bombings will radicalize the Lebanese population and generate new sympathy for Hezbollah. I've seen reports that lend credence to either conclusion.
Meanwhile, the UN is both urging that the Lebanese government take a more active role in disarming the terrorist militias attacking Israel, and that an international peacekeeping coalition be deployed to police the Israeli/Lebanese border. Israel has rejected the latter thus far. Once again, I'm torn. On the one hand, an international peacekeeping mission could do wonders in this region, if it does it's job and actually roots out Hezbollah. Israel's greatest fear, though, is that Hezbollah will take its cue from uncountable other terror organizations that have managed to operate with impunity from behind the shield of UN Blue Helmets, launching attacks and hiding behind the UN to protect from counter-strikes. This trick, unfortunately, tends to work exceedingly well, so from Israel's perspective allowing the UN in does nothing to make them safer, but does prevent them from actually defending themselves. So they're understandably less than enthusiastic at the prospect.