said by nwrickert :

I suggest that you create a public/private key pair, and test using that for logins with ssh. When you have that working, configure sshd so that only public key authentication is allowed. That gives additional security to the use of ssh.

And yes, you should be able to do most administration via an ssh connection.

If you are running your own linux system, with any kind of accessible service (apache, sshd, etc), you could have crontab on your mother's system automatically connect to your system every 15 minutes. It doesn't have to do anything after connecting, other than disconnect. That will leave you a trail of IP address changes in your logs, and you will have a good chance of having the current IP on hand.

said by Paulg :

Ive not had good luck with the dyndns updater built into the linksys firmwares, I ended up walking my dad through installing the updater on his PC after the router-based updater failed for the 4th time.