Keep in mind that DNS changes don't happen instantly. Usually 4-8 hours is enough time, but it can run longer. Changing a redirect is effectively a DNS change.
To completely understand the green checkmarks on whatsmydns.com you might also need to analyze what IP it's resolving.
As far as misunderstanding something, you appear to have unknowingly created the original problem yourself by putting a re-direct on the new domain, not realizing that would change the ability for you to work on the new site. Then I think it's further complicated now because your changes didn't immediately fix the problem. Another compounding factor could be that browsers tend to want to cache redirects as well.
Two things to check since Ipstenu reply also indicates she couldn't find the DNS entries as was wondering where the domain was registered. First make sure on the manage domains page of the panel, it says "fully hosted" in the web hosting column associated with your domain. If you were able to do a one click install it had to have been set that way at that time, but you may have changed it since. If you did change it since and need to put it back, make sure that you specify the same USER as before so that apache will be able to find the previous one click install. Second, it appears IpstenU though the domain is registered elsewhere, if that's the case have you set the dreamhost nameservers? they are NS1.dreamhost.com, NS2.dreamhost.com, NS3.dreamhost.com.
Finally, if you want the ability to have the re-direct in place, while you develop a new site here are a couple of wiki articles:
Actually.... Thinking about your specific case: In this case I don't think I would use the methods listed in those two articles. You have a new domain name, that you want to temporarily point to an old domain.
In THAT case, I would set the site up as a normal new site on dreamhost. After that is working, I would use an .htaccess redirect that redirects everyone except your IP. It should be a 302,303 or 307 redirect -- I'm a little confused which is the correct one these days. Since I don't have the exact recipe in my 'known to work on dreamhost' .htaccess library, I'm going to leave it someone to give you the code if your interested in taking that route.