I think you need to move the whole folder structure into Dreamweaver. Although I just normally strip out the Flash from the Lightroom Gallery and put it into a custom HTML file, rather than modifying the Lightroom one.
When in Dreamweaver, drag the gallery's "index" file into the root folder of your website. Dreamweaver should automatically update any links I think, but either way, you will either have to make sure the gallery's index file is in your root directory; ie where your current homepage "index" file is, or setup a redirect in your server's control panel....or integrate the gallery into your homepage somehow! lol