DNS in routed and dialup connections

This is basically a request to understand the differences (if any) in the
way that the AS/400 handles DNS during connections over the Internet via
routed and dial-up connections.
We have the following scenario: (its all SSL but I don't think that matters)
If we connect to a remote system (via the Internet) using dial-up PPP
connections, where the DNS is configured as dynamic, and the routing is
defined as 'add remote system as default route', everything works fine.
During the TCP negotiations, the DNS is specified by the remote system. This
is a private DNS used only in this connection.

If we connect by an existing routed link to the Internet, sometimes we can
not see the URL's within the remote system. i.e. it <seems> that we are not
using the remote system DNS.

So does dynamic DNS work differently accross a routed connection ?
Does the AS/400 use a 'list' of DNS's and go down the list looking for a
'hit' ?
  -- If so, is there a way of ensuring that the negotiated DNS in my routed
connection gets onto that 'list'

Thanks,

Regards

Ian Patterson
Grange Management Consultants
tel 01947 880458
www.grange-systems.co.uk