You leave a number of unanswered questions, for example will nameservers for other.com be left pointing to "other host" and at "other host" do you have complete control of your .htaccess?
What I would so (assuming you're trying to get rid of "other host" completely):
1 - add "other.com" to the dreamhost system using manage domains, set it for "fully hosted".
2 - put an .htaccess file in the root for other.com with a 301 redirect to http://www.main.com/newsite You can find some examples here.
3 - change the nameservers for other.com to ns[1,2,3].dreamhost.com (this change can take up to 3 days to occur worldwide).
4- optionally, later you can transfer the registration.
You can also in dreamhosts system combine steps 1 and 2, and simply add other.com to dreamhosts system as a redirect. (that is, don't fill out the "fully hosted" section of the form when you add other.com at dreamhost, but scroll down and just fill out the "redirect" section.
If the "other host" stays in the picture you have to live with capabilities they give you. you may just be able to drop an .htaccess in there to redirect but it might be different if they restrict you, use a different O/S, don't use apache....etc.