Don't send email from your own server

Did it ever occur to you to give your mother an account on your own mail server? If the problem is communicating, using e-mail, with your mother, then that would be an easier solution path than trying to get Google to care about your mail server.

If you configured your server to use SSL, which you absolutely should do, then you would have the added advantage of secure communication as the message would never be sent in the clear over the open Internet.