So when you say "I have a different name and password for each wordpress site" are you talking about the wordpress dashboard, or the ftp/shell login and password? What's important here is not the wordpress dashboard login, but where your files are actually stored, that being under one user or two. Did you use the dreamhost one-click installer to install both? or how did the sites get set up originally?
If you don't know the difference between relative and absolute then I'm sure you have used absolute, because wordpress tends to be that way on it's own. A relative link is formed something like ./images/blahblah.jpg and doesn't care if you change the structure above it. Definitely easier if you are going to move the location around later.
For the record, the sub-domain structure is much easier to change over, than the folder structure that you have. There are numerous threads with how to do the sub-domain changeover in the forum. Yours is not a lot different but is going to require using the shell to move folders around rather than just a few renames. Actually tho some ftp clients do have a 'move to' function. Do you have an actual FTP client installed on your local computer? If so, which one? Do you also have a telnet/ssh client like PuTTY installed locally?
(I'll also add a note to others here that my replies will be slow coming today after this one... so if someone else wants to pick up helping jacques_222 please feel free)