Both the systems cannot be in the same domain. One is production network.

Our system admin is so adament about this windows authentication and according to him there should be a way to do it.

Actually I can open management studio or odbcad32.exe from command prompt (Run as)using other windows domain account and then if I connect to sql server with windows authentication, it works. But the problem is, if we are using statistical tools like jumb then we cannot give the dsn name in that program. In that case connection will fail.