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.

I know I make it sound like I'm only ever emailing my mom, I thought it would be funny to write the story around that narrative, but of course I use email to communicate with other people as well.