It appears that everything is working fine for you, so I'm not sure I'd change anything at this point. If it isn't broken, don't fix it rule. However, I'm not sure what kind of codes are being fed to search engine spiders. I question why the web host set up a "redirect" and if that will cause problems for you with search engine spiders being upset about redirects. Don't they have access to setting anything up themselves with the web host account they have, then you could set it up the way you want it set up. I have access to settings for IIS through my web host, so I can set whatever I want. When I set up a domain and install dotnetnuke, I just have the appropriate domain alias set up in the host settings and then have IIS path for the domain set to the directory dotnetnuke in installed in. I'm not sure if you can or cannot have two domains point to the same path. But I don't think you'd want to have a domain redirection set up to have the "live" domain redirect to the "test" domain. That seems a bit like taking the scenic route and I don't know what if any extra time would be added to page loading with that type of redirection. Or did the web host mean that they set up the live domain to point to the same host directory as the test domain did? That would be a more direct approach. And setting the path or changing the path in IIS is immediate change, you don't have to wait for things to "propagate" like you do when setting up a new domain name or changing the DNS settings.
Anyway, I'd find out exactly what the web host did and if there are any problems that might occur because of the way they set things up, ie page loading time, redirect issues with search engine rankings, etc. I'd really want clarification as to what they did and what is really going on in the background of things. It just seems absurd to have domain1.com as a test site, then redirect domain2.com to domain1.com, then have some other trick to have it still display domain2.com after redirecting to domain1.com. Why not just have it all go through domain2.com to begin with and not have all this redirect crap going on? Or is that even what they did? Are they talking about redirection within DotNetNuke or are they talking about domain name redirection? That's two different things altogether.
But, again, it all appears to be working well right now, and I'd be hesitant to make any changes even if you are an expert and know what you are doing. It's one thing to mess up your own site, but another to mess up a clients site.
Anyway, I don't seem to have given you an answer, just more questions, but in order to know what you need to do, you need to have those questions answered fully and extensively first. Maybe you don't need to do anything at all, it just depends on what exactly the web host did, what settings they changed and why and how. I hope this is of some help, though.
Rick