I know you asked for free, but Fog Creek's CoPilot software is another option.
https://www.copilot.com/
I think it's something like $10 for a day's use, but there's nothing to install and it's supposed to work through NAT and firewalls. I haven't played with it yet (I'm basically waiting for my most technophobic relative to need help to try) but it looks promising if the person on the other end of the phone isn't up to installing remote access stuff over the phone. I don't know if it's possible for you to make a trip to her PC to set up remote access stuff in the first place. I just noticed they have subscription plans now as well, with a number of minutes per month (or pay-as-you-go).
When I started doing family tech support, nobody wanted to chip $$$ for me to drive to their homes, or for when I'd spend hours on the phone working with them. (They didn't even want to pay for shipping when I'd order parts for them) When I was unavailable for a while they found out how much it cost to hire somebody to do what I was doing; now they have no problem covering tools I need to help them. Perhaps if your mother needs regular help, she'd consider it worthwhile for HER to pay for something like this (or PCAnywhere, or other software) to help you help her. In other words, she buys you remote access software you can use for other purposes; out of the deal SHE gets better tech support.
Of course, my mother ran her home business with her PC at the time. If your mom's just playing web games and downloading funny pictures, she may not jump on the idea.