I think a lot of people are projecting 21st century attitudes towards nuclear weapons onto 1930s people. Using nukes on Germany and Japan wasn’t even considered a moral question by US planners, and they weren’t considered doomsday devices, just another big bomb. Unless the scenario postulates some kind of pre-WW2 nuclear exchange, I don’t see any reason they wouldn’t be used.
Chemical weapons were different - less than 20 years before, the major powers had been in a brutal war which used chemical weapons, and had signed a lot of treaties about their use. All sides had large stockpiles and countermeasures ready to go, so no one could get a significant surprise advantage from deploying them. Chemical weapons tend to slow down operations, so would have been highly detrimental to Germany during her conquests - plus there were no effective gas masks for horses, and the German army relied on horse transport, further hindering German offensives.
Also there was no concept of linking Nuclear-Chemical-Biological weapons like there is today, so nothing about using ‘NBC weapons’ and triggering a specific response fits in.
OTOH, people seem to be vastly overestimating the effects of nuclear weapons. If the weapons in this scenario are like what was developed before 1950 in our time, they are big, bulky, and hard to deliver to a target. There were no ICBMs or submarines, and no thing that would fit in a suitcase or artillery shell. They would have to be delivered by large, slow, vulnerable bombers, or driven directly to target by a ship or freight train. One strike would not wipe out a city like London, Berlin, or Moscow, and while deployed tactically would trash a target area, they wouldn’t wipe out an entire army, and any distant strike would be risky because of the lack of delivery systems.
I think you need to specify the parameters of this scenario a bit better before there can be much meaningful discussion. What does the delivery and manufacturing technology look like (there’s a huge difference between 1948, 1950, 1955, 1960, and 1965)? How many bombs and how much material to make more do various countries have (With nuclear weapons known, controlling supplies of uranium and plutonium becomes a major objective)? It’s likely to radically change the pre-war diplomacy and industry too.