Sendmail 8.8.7 as a back up mail server

[Stephen Swavley <Sswavley swavley com au>]

 I had a system running RedHat Linux 4.1.  I was using this system as a
secondary mail server.  This was a straight installation (i.e. no
tweaking).  I have installed RedHat Linux 5.1 over the top of this and
now it won't behave as a secondary mail server.  I started receiving the
message:

reject=551 <auser mydomain com au>... we do not relay

So added the domain name into /etc/mail/name_allow and then I got the
message:
SYSERR(root): backup.mydomain.com.au. config error: mail loops back to
me (MX problem?)

So I added the domain into /etc/sendmail.cw and got the message:
<auser mydomain com au>... User unknown

I have had great difficulty in finding any documentation on setting up a
secondary mail server and getting around these problems.  It would seem
to me that the solution must be quite simple, but what am I doing wrong?

Also, I house multiple domains.