Yugoslavia actually had a nuclear weapons program, but it was cancelled in Sixties for an unknown reason, possibly to do with improving relations with the USSR
The reason is not unknown, Yugoslavia embraced the world cause of nuclear disarmament within Non-Aligned Movement framework. Add to that it was expensive and required far more resources than provided by the government. It was pursued since 1948, paused between 1966 and 1974 and cancelled in late 1980s.
he Eastern Europe might be looking quite different, depending whether Yugoslavia maintains cordial relations with USSR, or since they are a nuclear power anyway the americans & co ar trying to court them into the anti-USSR camp after they get the bombs (seventies, eighties?)
OTL USA tried to get Yugoslavia to join NATO but that was not possible due to ideological and practical reasons. With nuclear bomb, there is even less incentive for Yugoslavia to do so.
EU/NATO countries s** themselves if the yugoslavian government politely reminds them they have nuclear weapons and interfering in their internal matters is not such a good idea.
A nuclear program will make things better for Yugoslavia. International community will be more concerned with Yugoslavian internal affairs, bolstering its economy and federal government since the 1980s, possibly preventing the rise of nationalism. Yugoslavia continues to exist until mid 1990s, reformed as a confederation, and the nuclear program is possibly agreed to be dismantled in return for economic support and political rights for minorities guaranteed by the international community.
Threatening international community with nuclear weapons will only make the country completely isolated with sanctions much harsher than OTL. Using nuclear weapons in a civil war will invite military intervention to eliminate any possible remaining nuclear capability.
Would the Serbians end up with the arsenal after Yugoslavia collapses? If so, they probably nuke Sarajevo during the Bosnian War.
That is just plain ASB.
Tito ordered the creation of Yugoslav nuclear bomb as early as 1948, following the Tito-Stalin split. This was followed by founding of three nuclear instituted in Slovenia, Croatia and Slovenia. Between 1948. and 1953. over 282 billion dollars were spent on nuclear research.
Accordign to document from May 1953. the primary goal for Yugoslavia is to develop nuclear weapons with the secondary objective of nuclear power. The same document blamed bureaucracy for making the effort incredibly hard, citing difficulties with getting heavy water from Norway. USA intelligence noticed as early as 1954 that Yugoslavia is pursing a nuclear research plan.
Nuclear partnerships were made with Norway and USSR - Belgrade institute was expanded several times, getting a research reactor in 1959. built by Soviets and supplied by Soviets (thanks to Khruschev). By 1962. Yugoslavia acquired technical plans for building a plutonium enrichment reactor from Norway, including some of high grade plutonium by 1966. The factory was never built since the project would not net results within 10 years and Tito became the world champion of Non-Aligned Movement, publicly supporting nuclear disarmament.
The project was reborn after India detonated its own nuclear bomb in 1974. After a secret meeting, peacetime nuclear research program was dramatically boosted in order to cover military program. At the same time, first Yugoslav nuclear power plant was being built near the Slovenian-Croatian border. Official propaganda even hinted that Yugoslavia might reconsider its nuclear stance due to nuclear monopol, lack of world wide agreement etc.
However, a significant increase in funding was only started in in 1982 under Branko Mamula, federal defense secretary. Plan B (11 peacetime nuclear energy projects) was supposed to mask Plan A (nuclear bombs). Plan A was directed in the Belgrade research institute, but all three nuclear institutes (Zagreb, Ljubljana and Beograd) collaborated on it. For example Croatian institute got the goal to develop neutron components (research polonium, berilium, alternatives, acquisition and so on).
Program A was shutdown in 1987 after federal government started to face problems and disruption from the Serbian nationalists. Program B was stopped de iure with new federal law banning new nuclear powerplants. At that time, Yugoslavia had 50 kilos of uranium usable for a bomb, and 10 kilos of enriched plutonium. IAEA monitored the reserves and the remains of the material were removed between 2002 and 2010.
According to physicists involved, Yugoslavia was nowhere near a nuclear bomb on its own - the most optimistic estimate gave 2010 for a prototype with spending increases. Yugoslavia would need to acquire or share date with some other country, perhaps somehow entering a joint development program.
According to OTL laws, nuclear weapon would be in hands of federal government and army which means it would end up under Serbian control.
This would have interesting butterflies - the USA would carefully not write off Yugoslavia as an area of no strategic value. It would be even more of a testbed for the possible breakup of USSR, as in OTL. The USA would be putting firm support behind the reformist federal government after Tito dies, along with Europe, discouraging Serbian nationalists and then giving stronger support to a peaceful secession process of various republics, with the firm goal of getting the nuclear weapon removed during the nineties in return for economic aid and guaranteed protection of minority rights.