DA makes the presumption, perhaps incorrectly, that some people will type in
www.example.com as their domain name, and so drops it when creating the domain name, and then reads it for webservice. Why? So mail to example.com will still be delivered.
It's easy enough to solve your mail problem if your user control panel has a link for
MX Records; you can simply uncheck the checkbox for mail for example.com, and change to a different mailserver.
And creating subdomains is easy, too, though perhaps not intuitive.
You click on
Subdomain Management and create (for example
joe.www as the subdomain.
The problem occurs if you want to get mail at the subdomain names. That won't work because DA doesn't set up mailboxes for subdomains. If you want mail for the subdomains, then you have to set them up as if they're entirely new domains.
To do that you have to make sure your hosting plan allows enough domains for your needs, and then create, for example,
joe.www.example.com as a new domain.
Of course since the main domain is on a different server you'll either have to manage nameservers for
www.example.com on the nameservers hosting
example.com, or else create all necessary DNS records on the nameservers hosting the zone file for
example.com.
Jeff