How could we get Italy to be neutral in the Cold War like its neighbours Austria and Switzerland? POD after WWII.
I really don't see why Italy was part of NATO. It's not as if the Soviets were going to invade them.
Italy joined NATO because the USA needed military bases in the peninsula. Let's be clear, when Italy joined NATO, 1949 IIRC, the foreign policy was strictly pro-american and it could not be any different since the reconstruction depended on the Marshall plan. USA needed the bases in order to control the mediterrean, since, as Mussolini said, Italy is a great "unsinkable air carrier". With a good fleet and air force (which the newborn NATO had in spade) you can control easily the whole sea. Italy was also useful to keep tabs over Yugoslavia.
In 1949, besides, Spain was still under Franco's regime and unavailable by NATO without some seriouos politic acrobatics, Greece was in the middle of an armed struggle with comunist partisans and Turkey still considered neutrality a better choice (they joined only in 1952 alongside Greece).
In exchange for her partecipation, Italy gained a fast track in the foreign policy, being "rehabilated" faster than Germany and Japan. Just to make an example, the italian army was rearmed well before the german one. It also played a part into the attribution of the "contested land" as Trieste. Finally Italy gained protection from Yugoslavia: the possibility of a conflict were low, but it would have been quite ugly for both the nations.
Please note that the italian goverment of the time was glad to be part of the NATO, not only for the above mentioned advantages, but also because lent them a protection against a possible communist uprising.
Switzerlandand Sweden were neutral during WW2 and had made of their policy of absolute neutrality their best shield. In other words, USA had no strong enough leverage over them.
Austria is a different kettle of fish. First it was an occupied country until 1955, when Russia and USA reached an agreement over her future: independent, but absolutely neutral. Neither of the two blocks would have accepted a different solution. Austria was in effect used as "neutral ground" during cold war.
In essence is quite difficult to have Italy not to join NATO, since it was a profitable step for both the parties involved. A possible POD could be to butterfly away the Cold War and so the need for NATO itself, but with a POD after 1945 seems to me a bit tricky (Stalin dies early and his successor is a reasonable guy? Mmh, bit far fetched).
As for having Italy leave NATO after 1949, let me say that it would be quite difficult.
First: having the communists in the goverment won't do the trick. If at any point in italian history between 1948 and the end of the seventies, the PCI had enough votes to gain the control of the country or become part of a coalition the only result would have been a military coup followed by a bout of civil war with a possible military intervention of NATO troops. There were back up plans in case of such evenience.
Second: the mutual need that made Italy join NATO were well alive until the fall of comunism in Russia. The italian politicians had too much to gain from this alliance to let it go. And there was no DeGaulle in Italy post-war.
In order to have Italy leave NATO and follow a neutral independent policy, we should have the USA commit a Huge diplomatic blunder, a slap so strong that no goverment, no matter how weak, could ignore. It must be the USA since no other member could cause such decision (at very worst, Italy would follow Greece example and retire troops).
A possible timeline could be the following:
In the night between the 7th and 8th december 1970, Junio Valerio Borghese, ex-commander of the Xa MAS, tried to seize power through a golpe. The plan made use of several NATO procedures in case of soviet invasion/ communist uprising). OTL the coup was halted at the very last minute (a group of soldiers were stopped just outside the National TV gates, while another group had already seized the armoury insiude the Minister of the interior), because the political support to the action and the CIA's assent was called back. Later it was discovered that the whole plan was a rrouse to let the current goverment declare martial law.
IATL, somethings goes wrong. The conjurates are discovered and fightings between them and carabinieri, loyal military units and police erupts. Unable to rein in his men, Borghese joins the fight, but he's mortally wounded, while most of his officers are captured and interrogated. Soon the truth comes out.
Initially the goverment tries to keep the lid down on the whole affair, but part of secreted documents are leaked to the free press. The public uproar is incredible: civil war is avoided but a narrow margin. The left in Italy is on warpath and gaining more consents every day.
The american president Johnson declares that the whole operation was a personal initiative of the local CIA officers, but his protests fall on deaf ears. The institution of a ad hoc cometee by the american senate is seen as an attempt to "bury everything under the sand".
Unable to salvage the situation, the italian prime minister, Mariano Rumor, decids to ride the tiger. In a public speech to the nation, he annouces that since the alliance with the USA was marred beyond salvation, so he had no other choice than announce that Italy was leaving NATO...