Remote access will work one direction, not the other

I'm trying to figure out how to remotely access my mother's computer so I can
help her learn how to use it. My dad used the computer before he died, and I
am not all that familiar with it. I am trying to use the remote assistance
method through messenger.

Both machines are running XP Home, and both have Messenger version 4.7.3001.
I have turned on the "Allow Remote Access" function on both machines, and
disabled the known firewalls on both machines when trying to connect.

So, if I am using Mom's machine, I can remotely access and control my
computer, but using my computer, I am not able to remote into Mom's. So far I
have not been able to find any other security software on her computer that
would be blocking me, and I have made sure the Windows firewall is turned off.

This is exactly what happens:
From Mom's machine I "Ask For Remote Assistance"
From my machine I "Accept", then get a message saying "A Remote Assistance
connection could not be established. You may want to check for network issues
or determine if the invitation expired or was cancelled by the person who
sent it"

I am working with the computers side by side, so so the invitation is not
expiring. I imagine I need to make some other change to the network settings,
or maybe some other security setting, on Mom's machine, but have no idea what
it might be.