I suggest TeamViewer.com. Since you are using older versions of Mac OS X, you may need to get an older TeamViewer.com version
<http://www.teamviewer.com/en/download/dyngate.aspx>
TeamViewer.com is very good at making connections over the internet.
The biggest problem with making connections over the internet is getting through the home router. This is where TeamViewer.com excels.
If you do not want to use TeamViewer.com, or have issues with getting an older version to run, I would not use Chicken of the VNC, since Mac OS X has its own built in screen sharing.
On Grandma's Mac, System Preferences -> Sharing -> Screen Sharing
Then setup up iChat accounts (this can be free AOL Instant Messenger (AIM) accounts; maybe even iCloud accounts, but I have not tried them on Leopard and Snow Leopard, so I'm not sure)
Now you start an iChat session, and one of the iChat options is share my screen.
Another advantage of iChat is that you can do audio sessions with Grandma, or video sessions, and just plan text messages back and forth. If using an AOL AIM account, you can use other messaging clients on other computers, smart phones, tablets that also speak AOL AIM protocol to send text messages to Grandma.
If you do not want to use iChat, then there is the build-in Mac OS X screen sharing. But to do this without iChat to get through home router, you will need to configure Grandma's home router to port forward port 5900 (the VNC port number) from the internet to her Mac.
<http://portforward.com/> gives instructions on setting up port forwarding for a lot of different router makes and models.
Then you should get a free Dynamic DNS name from a service such as NoIP.com, and run a dynamic DNS updater on Grandma's Mac (you can download an updated from NoIP.com that works with their service). The Dynamic DNS name will deal with your Grandma's ISP changing her IP address assigned to her router. Then you ONLY need to use the Dynamic DNS name, instead of trying to find your Grandma's IP adddress.
If you do not want to use a dynamic DNS service, then you can have your Grandma ask a web server what her IP address is
Google: "What is my IP address"
or <http://whatismyip.com>
Then she tells you the IP address. Most ISP's do not change the IP address for a home very often, but after a power failure, or just because the ISP wants to, it can be changed, so be prepared for it to change.
Good luck.