Yeah, I've never had much use for Apple Remote Desktop (even when I
had a legal copy). I've always gotten just as much use from this application:
/System/Library/CoreServices/Applications/Screen Sharing.app
You can find it by giving "/System/Library/CoreServices/Applications"
to the Finder's "Go to Folder..." command. I use it enough that I've dragged it
into my dock to make it easier to find 
It's great for connecting to other machines on your LAN (e.g. connect to
"foo.local" to connect a host called "foo" ). Or if the other Mac is fully on the
Internet (i.e. not behind a router that does NAT IP address sharing or otherwise
blocking your connection attempt) you can connect by giving that Mac's
IP address to the prompt.
Also ... if you are both have "Messages" working well, then in the chat window
with your mother, there will be a little circled "i" button in the top right of your chat window.
If you click it, you should see a row of icons that are labeled: call video share mail info.
if you click on "share", you should see options to share your screen, or request the remote
user to share their screen. Once connected you can decide whether to control or just
observe the remote machine.
It's more than a little tricky to use (often the share button is not clickable), but ... I hope
this helps and doesn't just lead to a lot of frustration.
Good luck
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