Right, Well first of all lets ignoire dear old Winifred. Her part in the story adds a certain charm but if you're looking for a rational explanation then the fact that your mum talks to dead people is unrelated to how a machine can operate briefly in the absense of a power supply.
The answer may lie in capacitence. Nowadays safety standards tend to mean that power capacitors feeding electirc motors in similar devices have a resistor attached in parallel to slowly drain the capacitor after it has been switched off. However I do remember Watchdog demonstraing a number of appliances where the capacitors had allowed the machines to "come to life" unexpectedly whilst detached from the mains even with all the switches in the off position. The specific example I remember was of a food processor which span up whilst the owner was washing the blades.
You did mention that the sewing machine was old so this is certainly a possibility. However the amount of energy stored in capacitors could only run the machine for a few moments. A sewing machine requires only a small amount of energy - as demonstrated by the existance of handheld battery powered versions, so perhaps rather than just a quick jerk there may have been enough oomph to spin up the flywheel you see on older machines.
Pulling figures from thin air I'd sugegst that anything over a minutes operation would suggest this posibility unlikley but a detailed examination of the machine in question could perhaps put a more accurate number to this time.
It's certainly a more pleasing explanation than you mother being a fantasy prone old bat whose husband humours her for an easy life. However if it turns out that your mum is reporting that the machine was operating for longer than capacitance would explain then we should be allowed to assume that a little bit of embelishment on her part is to be expected.