I might be confused here. But you don’t need to register your subdomain with your other register, just go to the admin panel of your dreamhost account.
select under the main menu
Domains >> Manage Domains
Click on Add Domain / Sub Domain
type in the subdomain in the Domain to Host: subdomainname.yourdomain.com
then click on the ‘Fully Host this Domain Now’
If this isn’t what you want, explain a little further.