Let me understand this better, you want to create a second repository on another server, which happens to be in a different domain, correct?

So here is the thing with Workflow Designer, you will need to have the workflow designer on a machine/server in the same domain as the workflow server. I am not sure if you can add workflow subscriber to listen for events on two servers at the same time.

You can always export out your workflows though, and import them to the secondary server. This is not that uncommon but I do not understand the rest. Are you hoping to have your test environment as a mimicked copy of your production repository? I mean this in the way that as users add documents and make folders and such inside the production environment, you want these things to appear inside the secondary repository?

I guess if that is what you were thinking, you would need to set up a connection profile and use the "replicate Entry" activity to replicate any new entries in the production environment to the testing environment. I am not sure though what would be the option if you wanted it to also have the latest revisions of documents from the production environment. That would be a little trickier, if at all possible.