Peter helped me resolve this one offline. Essentially it boiled down to this:
We are using the iFinity.FriendlyURL url rewriter. DMX, then when clicking on the "+" in the treeview, or trying to open a document was attempting to open a link that was in turn being redirected away from the page the DMX module was on.
The resolution was to add "DesktopModules" to the donotRedirectRegex attribute of the iFinity provider. The code looks like this in the web.config (See DesktopModules added nearly at the end of the code string).
Thanks for all your help, Peter, and bringing this to a successful conclusion!