Have you tried opening "Assem 1" and performing a File > Pack & Go. Give the new files a prefix of your choice.
When you open the copied assembly file, the in-context relation should still be there.
Hope this helps,
Pretty much tells you it won't work, did you consider doing a save as copy or pack and go. I'm not sure what your approach is or what your trying to accomplish. SolidWorks doesn't like the same name files etc..
There are many different ways of doing top down modeling because of the amount of users and industry, what I do here is highly possible that it won't work in another industry, like electrical etc...
Attached is a rough draft of my workflow, which should work for what you want.
Solidworks Work Flow.pdf 959.4 KB
You can select the parts/assy's in the feature tree, then right-click, select "form new subassembly" from dropdown menu.