The htaccess part of my previous topic did have to do with this. The CNAME part was a completely separate problem I had that I did end up solving using htaccess.
I did try changing the web directory of my subdomain from /home/username/sub.domain.com/ to /home/username/domain.com/dir/. That did not work. It just caused a bad_httpd_conf error to be displayed.
On a previous host I was on, they had a section in their panel called Virtual Sites which would take a subdomain and map it to a directory. When I moved to DreamHost I was trying to replicate that functionality.
Edit: Looking over the options in Manage Domain, it seems like I am not able to do what I’m trying to do. If the panel allowed me to mirror a subdomain to another domain’s directory then I would be able to achieve my goal. It seems the panel only allows mirrors of another domain but not of a domain’s directories.