When you install TV on your moms computer it will present you with a teamviewer ID.
When you start Teamviewer on your machine you click on the "remote control" tab and type the 9 digit TV Id that appears on your moms computer in the "partner ID" box. (You will also need the random password that is generated on your moms system.)
then "click connect to partner", as long as you moms computer is up and teamviewer is running you should be able to connect.
My advice once you get connected to your moms computer go to:
Extra/options
in the box that opens check the box that says" start teamviewer with windows"
then in the left column click "security"
now add a password( twice)
and down a bit farther next to "windows logon" in the drop down, click "allowed for all users" and then access control, "full access".
Click ok.
Now you should be able to access your moms computer any time it is on, even if she is not there.
IF she has a windows logon password, you will need to know that if the computer reboots.