Her people's lives aren't under imminent threat. Raboniel isn't harming any humans in the Tower at the moment. Furthermore, she thinks Navani has already answered her question after the discovery of Warlight. After that, she tells Navani that she has earned her respect and can do whatever she wants, at least until Raboniel finishes killing the tower. It seems like a lot of the discussion since I posted this has centered around the notebook and what happens once it's discovered. While that does annoy me, my main problem is even before that, Navani does not stop to think for even a second about the obvious consequences of her actions. After the discovery of Warlight, Raboniel blatantly tells her that she omitted her true goals to mislead Navani, is going to break her promise to leave the Tower and continue working to destroy Navani's allies, and that Navani should not be so trusting (people keep calling Raboniel a genius, despite her doing her best to demonstrate to Navani that she absolutely should not be trusted). So at this point, Navani knows that:
a) Raboniel cannot be trusted and will happily omit the true implications of what she asked Navani to achieve her true goals.
b ) She knows that the most likely outcome by far is that the Sibling is unmade and the Tower falls, cutting her off from her allies permanently.
c) Her actions are being monitored. At best, her findings have no way of reaching her allies.
d) I can forgive her for not figuring out the implications of anti-Voidlight, but she does know it's a powerful weapon Raboniel wants. See point a.
Based on these 4 pieces of information, the blindingly obvious conclusion is that if you undertake research into this mysterious weapon, it will be discovered by an enemy that will abuse the weapon in some way. Sure enough, that's exactly what happens and Navani is somehow surprised at every step. I find it highly reductive to handwave away all of this as the result of "trauma" because there are many other characters in SA with tragic pasts who are manipulated in ways that are actually plausible (not to mention that of all the main characters except Adolin, she probably has the best life. She had a normal childhood, a good marriage initially which turned into a condescending one, and now has a loving family again that actively supports her scholarly ambitions anyway). Navani never stopped over the weeks she was working and thought, "Hmm, I have a loving family that supports me now but is in danger. Should I keep working on a dangerous weapon that will probably fall into the hands of enemy who has shown she will happily lie to and exploit me?" I think what you're saying is how it should have been written. If Raboniel had actually threatened people close to Navani, or perhaps pretended to go along with Navani so Navani could plausibly think Raboniel was trustworthy, then I would understand the storyline.