My 14 week-old Border Collie pup has started to try chasing cars since she began walking on the lead. I religiously carried her everywhere before she was "safe" to get her used to traffic, but it obviously looks so different from her level now and it seems her herding instincts have appeared early. Apparently this instinct, if it's going to appear, develops anywhere from a few weeks to a year old, which seems to fit with your mum's dog. You may find "Understanding The Border Collie" by Carol Price helpful. She covers the background to why collies chase and suggests how to try to break the habit, which may not be easy in a dog who has been chasing for a year, and will need persistence. When a car passes Abby now, I get her attention to do some heel-work, and as long as I have her attention she doesn't even glance at the passing traffic. As our walk continues she shows less interest in the cars. However we have to start from scratch on each walk, but it's only been a couple of weeks, her walks past traffic aren't long yet, and it's an instinct I'm trying to get through so I'm not expecting miracles overnight.
I know the consequences of a collie getting loose to chase a car doesn't bear thinking about. Good luck to your mum. I'm sure she'll get there.

LynnT