I see. You might have to go the route of dynamic dns. (Can you still get that for free?) I haven't used it in a few years. I think I used dyndns.org, if they still exist. There are clients that automatically update the DNS entries as the IP address changes. With that you would just use the domain name you assign to connect to her computer.
Otherwise you could get your aunt to tell you her IP address through the System Prefs before you can connect.
Of course if she is on dial-up she can't tell you over the phone, probably. So she'd have to use iChat or something similar.
Or if you want to get really fancy, you could theoretically set up a VPN that her computer automatically joins with yours, thus making the connection trivial. Someone with more knowledge about VPNs could say whether or not that would actually work.
Jim