I finally figured it out!

All I had to do was put localhost as the SMTP Server in Host Settings and change the type to anonymous and now I have each admin's email address as the sender for each parent portal!

You definately do not need an email relay server to have a different sender's email address for each parent portal. When you use localhost as the SMTP Server, DotNetNuke uses the admin's email address for all outgoing email messages for each parent portal you have setup.

So if you have a different domain name for each parent portal then you probably don't want the same admin email address for both parent portals.

I have Network Solutions shared hosting and would recommend them for hosting a manual installation of DotNetNuke because there hosting is excellent compared to GoDaddy.

I have all my domains registered through GoDaddy and host my DotNetNuke instance through Network Solutions.

The email address alone is not enough for a mail server to authenticate users. A user name and password are required. Both are needed for either smtp authentication or POP before SMTP. Which mail servers allow sending of emails by email address only? In such a case, it's not much better than an open relay because anyone then can use the mail server to send out emails if they only have to specify an email address.