Right, I'm just getting into a bigger and bigger mess and I'm getting upset now, because it's taking me so long and you're making it sound easy.
My site http://www.myparent.com has http://www.myparent.com/childsite_1/
I am traying to move childsite_1 to http://www.childsite_1.com
I have created the directory childsite_1 and removed the mapping of the http://www.myparent.com/childsite_1/
childsite_1.com is an addon domain of the hosting account.
Now when I switch to childsite_1.com it shows a 500 internal server error and when I switch to http://www.myparent.com/childsite_1/ it shows the install of my new stand alone site.
What it appears that you are saying, is that if I do the import I can click a check box to import images. Which, by the sound of it, are being pulled from their URL's. The way my setup is at the moment, this could never happen, because the URL it's meant to be pulling it to, is the URL it's already sitting at (but don't want it to be).
I'm pulling my hair out.