I don't think I would say she was "pivotal" on nuclear weapons issues — she did take part in the research, and was involved in several important studies (e.g. she worked on gaseous diffusion, and helped identify reactor "poisons"), but I wouldn't overstate her influence or importance there. It was, after all, a very big project; there are only a few people who really were absolutely pivotal or crucial to it. One short-hand way to think about it: if you take Wu out of history, does it change the outcome of the Manhattan Project in any significant way? I don't think it does. There are very few people who rate as "important" by this speculative, counterfactual narrative (a handful).

In any case, it is kind of a non-sequitur to pivot from that to the Nobel Prize issue, which is totally unrelated. The question of who should and should not get Nobel Prizes when there are large teams of possible people has dogged the Prize process for a long time. The prize she would have been most eligible for is her experimental demonstration of Lee and Yang's theory of non-conservation of parity. I have not seen anything that discusses the actual deliberations of the Nobel committee on this matter, but from the outside it looks like a tricky thing: you have the two theorists who postulate the idea, and then you had several experiments that demonstrate its reality. Wu's was one of the most famous of these, and maybe the first, and one of the most elegant experiments, but you also have other contenders, like Garwin, Lederman, and Weinrich's experiment showing the same thing (in partial collaboration with Wu as well, as their initial paper acknowledges) at nearly the same time. There were also less-heralded experiments done elsewhere.

Nobel Prizes in any given year can only go to three people. In situations like these, they have tended to be given to the theorists who came up with the idea that the experimentalists confirmed, not to the experimentalists. Can we imagine a world in which Lee, Yang, and Wu all three got the Prize for 1957? Sure. But we cannot imagine a world in which Lee, Yang, Wu, Garwin, Lederman, Weinrich, etc. etc., all got the Prize. In such situations it is typical, if unreflective of the way in which science actually works, for the committee to make a hard cut-off, essentially saying, "to resolve this issue we're only going to give it based on X criteria," which in this case appears to have excluded all confirmations. This is just one of the many, many reasons that the idea that Nobel Prizes adequately reflect scientific accomplishment, priority, or process is very incorrect; they reflect the complex and somewhat bounded system in which Nobel Prizes are evaluated, which only glances the broader question of worth.

On the contributions to the Manhattan Project, Herzenberg and Ruth, Their Day in the Sun: Women of the Manhattan Project discusses Wu's contributions a bit. On the parity issue, I found the discussion in Shurkin's biography of Garwin (True Genius) reasonably useful, even though as a whole it is a book with a lot of writing issues. I also am in the process (a few hours a week) of doing an oral history interview with a physicist colleague of mine who worked with Wu, Lederman, and several others at Columbia and Brookhaven as a graduate student on their parity conservation work, which has no doubt colored my thinking on it. :-) He reports that Wu was terrible to work with as a grad student (something he would say about a number of the Columbia luminaries) and he ended up avoiding becoming beholden to her, for whatever that is worth.