Yes WG could have gone against the wishes of the USSR, but it cant go against the wishes of of everybody USSR/GB/FR... (and potentially USA not to mention all of Europe's smaller nations)
Remember that even in 1990 Thatcher etc still didn't really want German reunification, early in the cold war in the 50s the attitude to Germany would probably be far worse?
No, it wasn't - strange as it seems. In 1950, lots of ACTUAL Nazis were pardoned in return for their help to fight the cold war. Just remember that Werner von Braun was a member of the SS and the technical leader of a concentration camp.
We should also remember that from the very beginning of the re-armament, Germany was allowed to take part in nuclear sharing, so all in all West-German nukes is not that much more a breach of taboo as happened IOTL. If there is a problem, then it's the lack of strategic benefit for the NATO: If Britain and America need more nukes, they just make more of their own rather than give away the potential.
OTOH France wants to catch up with Britain and the US to avoid being pushed aside in the NATO and might decide to let West Germany join their nuclear weapons programme. Indeed such an arrangement was considered IOTL: West Germany would have had its own nukes, but their development and production would have been on French soil.