One thing is easy to answer - I doubt that "myotherprivatesite.com" is a registered domain name and therefore no IP can be found for it.
When you use sendmail directly, what IP do you give it? If you give it 127.0.0.1 then this should work for you within AOLserver. If it is listening on another IP, then you must use that IP.
For simplicity's sake, make all your hostname parameters be whatever that correct IP is. Your complex logical names with "smtp.foo.etc" aren't going to work unless you can ping them from the shell (implying you've set up the domain name and the local machine within that domain, etc).
The "Not authenticated" message is a new one, to me. I think that whatever you did to get that message might actually be the right thing to do, and that the error's due to the way you have sendmail configured. It sounds as though sendmail got the mail, but didn't send it due to authentication (permission?) problems. This indicates that you're talking to sendmail OK, but sendmail doesn't like you, meaning it's not an AOLserver configuration problem.
So my advice is to replicate whatever got you that error message, and work on sendmail from there.
