Edit /etc/mail/sendmail.cf and add the appropriate entry in the section:
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# "Smart" relay host (may be null)
DSsmarthostname.domain.ext
To use AuthSMTP against your mail relay host, you need to edit your /etc/mail/access file and add something like:
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AuthInfo:smtp.domain.com "U:loginname" "I:loginname" "P:password"
where smtp.domain.com is the smarthost you're trying to send through and loginname and password is the auth info you need to supply to send mail through it. Once you've made those changes, you need to restart sendmail.
I'm concerned about your dynamic ip. Have you sorted how your are going to receive mail?
Regards,
Don