The two men had threatened the 45-year-old woman with what is thought to have been a taser-type weapon outside the family home in Oxford Grove.
Terrified, the mum had fled into a nearby flat and the men attempted to drive off in the VW Caddy - which still had its tailgate and wheelchair ramp down.
Unbelievably, having failed to start the car, the men hammered on the door to demand their victim come out to help them make their getaway.
The pair are understood to have escaped the scene in a dark-coloured vehicle that had been waiting at the end of the cul-de-sac.
Police have now appealed for help in tracing the would-be robbers, who had targeted the family last Wednesday night (August 24). The incident happened at around 11pm.
Det Con Rhett Collier said: "It’s hard to imagine a more callous act…trying to steal a specially adapted car that the family of a disabled lady rely on for her transport.
"The woman had just dropped her daughter back off at home, and helped her to bed, when she returned to the VW Caddy. One man pointed some kind of stun gun at her and made threats, while another banged on the flat door.
"The victim tells me that her daughter [aged 25], who heard the banging and commotion, has been left very scared by the incident and now needs additional night time care as a result. She has struggled to sleep since."
The two men are described as white and in their late teens or early 20s. Two accomplices are understood to have waited in the vehicle at the end of the road during the incident.
Officers urged anyone with information to search their conscience and get in touch.
"People who are prepared to stoop to such levels do not deserve protection," said Det Con Collier.
If you know anything about last week's incident, call officers on 101 or Crimestoppers, anonymously, on 0800 555 111.