Set up Sendmail as sending only server

I have set up where my primary fibre optical WAN access does not have any sending SMTP service but my fall-back ADSL service does. However, with most Internet Service Providers, the SMTP service access is "locked" to the IP addresses that the service knows about. Therefore I can not send SMTP requests to my ADSL service while using the fibre optical. I have then installed Sendmail on a CentOS 5.5 64 bit so as to allow sending SMTP request no matter what service is active.

My new problem is that I can not sending SMTP requests to email address on my own domain (receiving email server not in my offices!)

How can I configure Sendmail server to be a sending SMTP server only.