You've got some pretty misguided views when it comes to coding. Not that it's wrong, but there's a lot more to the whole web developer thing than just programs, especially if you want to make it in the industry.
Learning how to hand code HTML and CSS is a requirement. Period, end of story. I personally don't know this from experience (as I learned from the ground up), but learning how to design from a program like Dreamweaver isn't going to give you the whole picture.
The mechanic analogy is a good example. Dreamweaver is a tool, I use it sometimes myself to help automate some repetative code or the like. But without having an intermediate knowledge of how the code works on a site, the tool is useless.
I'm actually still learning, myself. Going to try to get into the advertising/graphic design sector as soon as I finish my general education requirements (CSU). Make no mistake, coding isn't a shortcut factory, but knowing how things work, and knowing how they work together. That's were the best developers come from.
And lets not forget design; as far as that goes, a few good books on the aesthetics of web design, and maybe even general art will go a long way in giving that 'professional' look that you so desire; because believe it or not, most of the professional designers I know (here in San Francisco) don't actually use WYSIWYG programs. I know one that still codes with Notepad. Says it makes him feel alive.