if you're trying to connect to a computer using RDP that's on the same local area network that you're on then you can connect with the local address.
if you're in a different building, and don't have any kind of VPN solution in place you'll need to do the following.
First, configure the router at your mums house to forward requests to port 3389 (the port that RDP uses), to the local address of your mums computer.
now you should find that if you make a request from your computer to the external (internet) address at your mums house, (which she can find by going to www.whatismyip.com
) you should get a login prompt.
you should also note that allowing ports to be forwarded to a computer exposes the computer on the internet, so anyone can connect to the computer, (obviously not everyone can log on unless they guess the password correctly).