You have to go through Layout. Make the scenes in Layout and then export the Layout file to dwg. Also SketchUp is absolutely not like other cad programs, it takes some getting used to.
There are some extensions that do dwg export, maybe look at those. SketchUp is kind of a base platform and most people use extensions to add functionality and tailor the experience. A larger part of the user base is NOT in the design build industry. 5D+ is worth a look, and pretty reasonably priced at $60 flat. This thread is devoted to it. Or maybe Schema 2D Projection for $14.99 is what you want, looks like you could easily export the generated flat geometry to AutoCAD. I may actually check this one out. I also prefer to draw 2D in AutoCAD, although many here would suggest just using SketchUp and LayOut and abandoning the AutoCAD overlords completely.
EDIT: I installed Schema 2D Projection and the extension is broken. I did email the developer with the error messages, but for now no good.