Has there even been a direct conventional war between two nuclear powers before? I expect that nuclear weapons are a deterrent of any war when both sides have them.

The problem with disarmament seems to be that imbalances arise, and the problem with armament seems to be that if hundreds of countries have them, there's a high probability of one of them doing something stupid/crazy/suicidal.

Yes, the Sino-Soviet border conflict of 1969 and the Kargil war between India and Pakistan in 1999.

That was an interesting conflict from the stand point of nuclear restrain. Territories were occupied, hundreds of casualties, open fire and fighter jets; yet no nuclear threats. I haven't read up on it but just looking at the outcome of the war.

Yes, that is another hotspot, but tensions between them have risen and fallen and neither party appears to be willing to commit to the end of the world. They are in an equilibrium of MAD.