Forget about Dreamweaver Design View. It's rubbish, and is very misleading. It's not a browser. A better approach is to open your page in a real browser, and each time you make a code change, refresh the browser. Lots of people come here having problems with Design view. It's just not a professional tool.
I've actually had really good results in DW design view, but you have to know its limits. It's easily confused by advanced (or crappy) CSS, and if you rely on it for all your work, you'll have unexpected results. Ralph's advice is best. Learn how to hand code.