It seems that you have a two-stage problem: how to get EA to open a specific model, and how to have EA display a specific diagram when the model is opened.
The second one is easy: open a diagram in EA (by hand) and then from the main menu choose Diagram | Set as Model Default. Note that this is not available from the context menu when you right-click the diagram; you must use the main menu.
[NOTE: I am assuming you have the Corporate edition of EA from this point on. A lot of the discussion involves models stored in a DBMS.
I am also listing the steps in a blow-by-blow - pretty long winded - fashion, since I don't know your experience level. Please stay with me.]
The first part is a bit trickier. I suspect - this is entirely without proof, so you need to check this - that you can create a command line with a file name following EA, and that EA will open that file. So far so good, if it works. But that would still handicap you if you need to open a model in a DBMS repository.
Here's what I'd do as an alternative.
When you are working with a model in a DBMS repository, EA allows you 'save' the file to an EAP file. If you do so, the EAP file does not contain the actual model. Rather, it contains the connection string that EA uses to open the DBMS model. If you later open that file from EA, it connects to the DBMS and opens the model from there.
So far so good.
If you were to invoke the file from the desktop, or a command line, or the Windows Explorer, Windows would identify the EAP extension and invoke EA to open the file. Thus, you'd automatically have EA start and connect to the model.
Better, but we're not there yet.
In order to get this to work from a URL, you might have to define a MIME type to associate the EAP file type in a URL with EA. Not difficult to do; check your browser settings.
Almost finished.
What about having EA open a file that's not in a DBMS repository? This is actually pretty easy. You can have EA open an EAP file as if it were in a repository; Microsoft Jet would be the repository 'engine' in this case. Just start EA - there's no need to open any model - and use File | Open Project to get the normal open dialog. Check the Connect to Server box in the upper right, then click the browse button ("..."). In the first dialog (Data Link Properties) choose the appropriate Jet driver - either 3.51 or 4.0, to match the one you have set in the Tools | Options dialog - and then fill out the rest of the dialogs. One of them will allow you to identify which EAP file you are pointing to. Now you can do the same 'save' operation as with a DBMS, and get the same result.
Please let us know how it works.
David