Intermittent problems seem to love you and naturally collect around you
Does your Mum's car have a diagnostic port?
Here's a few tips from a car guy ( I did service writing and managing in the late '90's):
1. All cars sold in the US starting in '96 are OBD II spec; among other things that means the diagnostic port is standardized in plug config, input/output data and even location.
2. You can buy a cheap reader from Harbor Freight for something like $35; it will reset too if you have a "check engine" event. Won't do advanced diagnostics, just reads the codes from the check engine light.
3. The diag port is visible just below the lower lip of the dashboard, within 6 inches of the steering column right or left.
4. IF the car has an in-tank fuel pump (common), you should put a 2 or 3 foot long piece of 2x4 in the car; then, if you can duplicate the problem you should smack the bottom of the tank with the board; many times this will unstick the pump long enough to get things running again, and pinpoint the problem as fuel pump related.
5. Does the car have a fuel filter, and has it been changed recently? A lot of times the filter will block, then unblock as the crud moves around.
I hope this helps.