Taking Redhat with the initial and default sendmail configuration.
Add your domain to be relay from sendmail:
vi /etc/mail/access
Connect:sendmail.mydomain RELAY Connect:192.168.1.10 RELAY
Compile the entries with:
makemap hash /etc/mail/access < /etc/mail/access
Change the following line in order to allow sendmail to listen to right IP rather than the localhost lookup address:
vi /etc/mail/sendmail.mc
dnl # The following causes sendmail to only listen on the IPv4 loopback address dnl # 127.0.0.1 and not on any other network devices. Remove the loopback dnl # address restriction to accept email from the internet or intranet. dnl # DAEMON_OPTIONS(`Port=smtp,Addr=192.168.1.10, Name=MTA')dnl
Now, and as unfortunately I do not access to my local DNS server, I would add my mail server to the host file:
vi /etc/hosts
192.168.1.91 domino2
and now, I add my name server domino2 to sendmail.cf as Smart relay host
vi /etc/mail/sendmail.cf
# "Smart" relay host (may be null) DSdomino2
keep in mind that Sendmail 8.13 having by default the Reverse DNS IP lookup feature, which would verify if the IP match with the domain that the helo at the initial SMTP transaction.
Restart sendmail
/etc/init.d/sendmail restart