Good suggestion.
Has anyone got any idea that would make the player actually want to dissolve the USSR? Currently I see no reason why the player would or would be forced to do so, and I think that if the player wants to stay as the USSR, it would be difficult.
War with nations wishing to secede from the union? Threat of war or sanctions from western powers due to the previous thing, especially over the baltic nations, which would also force the player to increase military spending, devastating the economy and all hopes for reforms. Offer the player chances for negotiating with nations that wish to leave, (the baltic nations should be next to impossible to keep within the union peacefully) opening the possibility for compromising with the republics, possibly puppetship, economic development or aid, or
democratization (What Gorbachev might have turned towards) with the possibility for creating a strong federation although with more autonomy to the republics than before (
http://en.wikipedia.org/wiki/Commonwealth_of_Independent_States).
Uprisings. Riots (dissent), economic stagnation since reforming the union is too difficult because of conservative communist resistance, and the growing threat of a military coup.
There were also two other countries than Ukraine (5000 warheads) which inherited nuclear arsenals, Kazakhstan (1400 warheads) and Belarus (81 warheads).
A few random suggestions for historical events, inspired by Wikipedia:
South Africa signed the Nuclear Non-Proliferation Treaty in 1991.
Pakistan did not possess nuclear weapons until 1990, when sanctions were imposed under the Pressler Amendment, requiring a cutoff of U.S. economic and military assistance to Pakistan.[28] In 1998, Pakistan conducted its first six nuclear tests at the Chagai Hills,
Indo-Pakistani Nuclear arms race starting 1998, and still ongoing at a slower pace, India and Pakistan doing nuclear tests simultaneously in 1998.
http://en.wikipedia.org/wiki/Agreed_Framework
North Korea's main reactor, where practically all of its plutonium has been produced, is a 5MWe gas-graphite moderated Magnox type reactor. A full core consists of 8,000 fuel rods and can yield a maximum of 27–29 kg of plutonium if left in the reactor for optimal burnup.[13] Often, North Korea has unloaded the reactor before reaching the maximum burnup level.
There are three known cores which were unloaded in 1994 (under IAEA supervision in accordance with the
Agreed Framework) A secret core, Core 0, may have been
unloaded between 1989 and 1990 and verification is needed to confirm North Korean claims that such an unloading or partial unloading did not take place.