HI,
iChat or Messages will let you do this is both ends have Screens Names (AIM based) or Jabber IDs.
In Messages or iChat go to the App menu > Preferences > Accounst and use the plus button at the bottom of ther list to add an Account.
In the add Account Pane chose either AIM (Includes some Apple IDs) or Jabber (Includes a Google options in the list).
Google Mail IDs work in the Google choice if you enable "Talk" in the Products at your Google account page (not the web mail login)
Facebook IDs can also be Jabber IDs if you enable "Chat" at their settings.
Use the Preferences > General section to Unlink the gathered Buddy lists (By default they are in one list in Messages).
The window Menu should now display a list of Buddy List accounts that can be displayed.
(Bonjour if Enabled, Jabber, Google and/or AIM). There is a Yahoo account but this will not Video or Audio Only chats which in turn means no Screen Sharing.
Once you have the Buddy list on Show you can add the Buddy name
(Press the + icon and choose Add Buddy (Or use the Buddies menu > Add Buddy) )
Having the list separate means you can add the right name to the right Buddy List.
Check you can Video chat (Screen Sharing needs the same Internet Connection minimum speed.)
You need to activate Screen Sharing in the Video menu.
This version is really an Audio Chat with a VNC connection along side
For this UPnP needs to be the method employed in the router to open ports as the VNC connection is on a random port.
The System base Screen Sharing is also a VNC connection.
It follows more closely to the Apple Remote Desktop (ARD) ports as it too, like iChat/Messages uses the ARD engine.
However instead on a Finder > Go Menu > Go to Server and typing VNC:// and a local IP or Browsing for a local computer you need the Public IP address of your mother's Modem.
The modem or router at her end would then need to point that connection to the computer (Port Forwarding).
The same would need to be done in your router for the return stuff.
(most routers have the first 1024 ports (or 65535) open but in this case the Screen Sharing app uses ports above this as does iChat/Messages).
iChat just handles it better once UPnP is enabled.

10:33 pm Sunday; July 28, 2013
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.4)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad
"Limit the Logs to the Bits above Binary Images." No, Seriously