What is your definition of Peacekeeper?

“peacekeeper” – 2. a soldier, military force, etc., deployed to maintain or restore the peace

I doubt that this is what is meant by the U.N. or the Europeans. I think they have confused the definition with this one;
“observer” – 1. Someone or something that observers
2. a delegate to an assembly

The commander of UN peacekeepers in Lebanon described the ceasefire between Israel and Hezbollah as "very fragile" and "dangerous" and said that an expanded international force would not disarm Hezbollah.
"The Israelis cannot ask UNIFIL to disarm Hezbollah. This is not written in our mandate," French Maj.-Gen. Alain Pellegrini, commander of the 2,000-member UN Interim Force in Lebanon, known as UNIFIL, told reporters at UNIFIL headquarters in the coastal town of Naqoura.

If France does return to seek to lead the peacekeeping force, where would that leave Italy's leadership offer? Apparently the Italians would only be in charge from the other side of the world;
A report in the Rome daily "La Repubblica" today says France has offered a dual command with Rome. France would continue to command the force on the ground in Lebanon through General Pellegrini, while Italy would take control of the UN Office of Peacekeeping Operations.
That means France would have operational command on the ground, with Italy given political control at the UN in New York.
All these details are due to be discussed on August 25 in Brussels when UN Secretary-General Kofi Annan meets with EU foreign ministers.

So the UN and Europeans seem to be insistent upon the French being in charge, as if that worked so well in Yugoslavia or in Rwanda.

A spokesman for the Italian Foreign Affairs Committee had this to say;
In the last few years, Italy, with the previous government, has had a more pro-American and pro-Israel foreign policy. The new center-left government is interested in acquiring a new role that is more focused on Europe and to be more active in the Middle East, including the rebuilding of our ties with the Arab world along with our ties with the government of Israel. This is why the new government believes that the strongly pro-American position of the previous government had weakened Italy on both the European and international scene.
So, by assuming a lead role in this conflict, the Italian government believes it can recoup some of these past losses. Besides, the withdrawal of troops from Iraq, which was decided by the new government, risked weakening Italy on the international scene.
And you will recall that last year, there was debate regarding the reform of the United Nations Security Council, which involved the possibility of making Germany a permanent member of the council. This would have further declassed Italy on the European scene. Italy believes that taking on a lead role here can help it reacquire prestige and status with regard to the United Nations.

Italian politicians may look forward to this chance to strengthen their international image but the Italian military seems to understand the big pile of shit they are going to be left standing in.
"If we must draw lessons from past experiences, then we must admit in all honesty that the operations commanded by the U.N. have turned out to be failures, in some cases a total disaster," Gen. Fabrizio Castagnetti was quoted as saying by Milan daily Corriere della Sera.
Asked why, Castagnetti replied, "Because the commander has his hands tied," Corriere della Sera said. "He cannot make decisions without consulting U.N. headquarters in New York."
The commander's "appeals to receive clear directives clash with the elephantine bureaucracy of the United Nations ."
"A mission under U.N. command creates a lot of problems. I will say so to the (Italian) defense minister," the general was quoted as saying.

Other nations also seems to have the idea that the humanitarian mission has priority over the actual job of peacekeeping;
The Department of Foreign Affairs (DFA) earlier said Manila is likely to send "non-combat" troops as well as medical workers to Lebanon, where the UN is trying to muster an international force to serve as a buffer between Israel and the Hezbollah militia.

Hezbollah has promised to cooperate with Lebanese and U.N. forces but has made clear it will keep its weapons.
Larsen said 2,000 soldiers had been deployed along the eastern border and the government aimed to boost that to 8,600.
"This fact that Lebanon is now forcefully establishing its authority will contribute to pave the way for troop contributors to come forward to a reconfigured and beefed up UNIFIL," Larsen said.

The 2000 troops of the current UNIFIL force have focused on putting out daily reports that show they have been demolishing unexploded ordinance, supplying water to the locals, reporting violation (principally air violation by the IDF), ground and air patrolling to “assess the situation on the ground and to monitor the cessation of hostilities” and accepting handoff from the IDF and handover to the Lebanese Army. They even went so far as to report second hand reports in the area of Baalbeck even though there are no UNIFIL forces in that area and therefore can’t provide direct knowledge of the event.

The demolition of ordinance is done by the UNIFIL-Mine Action Coordination Center which was added to UNIFIL after the Lebanese requested help in eliminating mines and unexploded ordinance in 2000. Just to show what kind of support a UN group provides the organization chart for the MACC Southern Lebanon which not only shows their current members, but also past members. The org chart starts with Serial #1, the admin/log Assistant, #3, the Genitor, and includes past drivers, Programme Managers, Finance Officers.

The UN has been involved in some 59 peacekeeping missions have they ever used force in any of them? Even if the rules of engagement give the peacekeepers authorization to use force in self defense, even prior to being fired on, how likely is it that they will do so? Just look at all the second guessing that goes on with use of force in Iraq and imaging how European forces will react when in a situation where they could fire or not.

Kofi Anan certainly is giving them a good example;
Secretary General: Let me say that the resolution does not require deployment of UN troops to the border. It indicates that, if the Lebanese government were to ask for it, we should assist. The Lebanese Government has not made any such request.
As to your question on disarmament, let me be clear that resolution 1559 asks for the disarmament of all militia, national and non-national, and this was reaffirmed in resolution 1701. The understanding was that it would be the Lebanese who would disarm. I think it is also generally accepted that the disarmament of Hezbollah cannot be done by force. It has to be a political agreement between the Lebanese; there has to be a Lebanese consensus and an agreement among them to disarm. In fact, before the war, this issue was part of a national dialogue going on in Lebanon; I hope they will return to it in earnest. Obviously, if at some stage they need advice or some help from the international community and they were to approach us, we would consider it, but the troops are not going in there to disarm. Let us be clear on that. The other question, perhaps I will defer that to you, that part of the question.
Resolution 1701 paragraph 11(f) calls for UNIFIL to support enforcement of blockade against arms smuggling from Syria only if Lebanon asks for help.

With the way that European nations have been giving Hezbollah status equivalent to actual nations how likely is it that they will provide any opposition to violations of the resolutions by Hezbollah;
"We have no problem with Unifil (UN Interim Force in Lebanon) as long as its mission is not aimed at disarming Hezbollah," Nasrallah said in an interview aired on Lebanese television. He added, however, that if Lebanese troops in southern Lebanon encountered armed militants, the national forces did have the right to collect weapons.
The UNHCR has the mission in assisting with supplies for relief, this should not be the primary mission of peacekeepers. Yet Resolution 1701 paragraph 11(d) calls for exactly this, not that their mission needs any further confusion.