Yep. That's all pretty much accurate. Though the idea that yellowcake is all THAT far removed from a nuke is open to debate - once you have the uranium in any fashion, your steps are pretty straightforward: refine to pure uranium, separate, mold the unstabe mass into a warhead, add the trigger, boom. Pretty straightforward, actually...the challenges crop up in the matter of scale: it takes quite a few centrifuges quite a lot of time to create the weapons-grade material, and those take up space and use power. In other words, you need a decent-sized hard-to-hide industry to make a nuke.
The whole nuclear justification never struck me as anythng more than BS, as did the missile stories for the same reasons (you need industry to build and support them). Chem/bio, however, is another story...