Set up FileOptions to open the restricted database automatically with a password that has the minimum permissions needed to supply data to your value list. The Read Only privilege set is probably all that you need.
To open that file with a different account and thus different permission settings, hold down the option key (macs) or shift key (windows) while opening the file, or put a button on the layout that appears when the file first opens that has a Re-Login script to open the log in dialog.
Come to think of it, you can also set up your "any one can open" file's File OPtions to auto enter an account and password defined in File 1 that matches to a "read only" account in file 2...
Let me know if my thinking is incorrect.
Is there a way to do this with the Edit Data Source to have filemaker login through there?
There is no such option in Edit Data Source.
I am suggesting setting up File Options from the File menu to to auto-enter an account name and password in one of the two files as a way to keep the Log In Dialog from popping up when the layout in file 1 requires data from file 2.