Go to http://whatismyip.com/
That will tell you your Internet
The 192.168.1.* addresses are the LAN
addresses of your computers.
You will need to set up port forwarding in your mother's modem/router to forward ports 5900-5909 to her LAN IP, and maybe open a hole in her firewall to allow this. See her modem/router's manual for how to do this.
I do the same with my mother's PC. She gets her IP address from whatismyip.com, phones me up, and then runs krfb
which allows me to control her desktop. Excellent for sorting out problems and demonstrating how to do things.
Edit: She is running linux, but there'll be a similar program to krfb