A court heard the victim pleaded with the attackers as she was ordered to get out of the car without her child.
She later described the incident as “a perfect storm of awfulness.”
Zahid Mahmood, 20, and Usman Mahboob, 18, targeted the woman outside her home in Burley, Leeds, on June 12 last year.
The woman was threatened with a knife by one of the men after she had put her son into a child seat.
He got into the vehicle beside her and ordered her to get out.
She was threatened with the weapon before eventually being allowed to get the 13-month-old child out of the vehicle
Mahmood and Mahboob then drove off in the Ford Focus.
They were arrested later that morning when a member of the public contacted police after seeing them driving suspiciously.
The court heard the woman has been diagnosed as suffering from post traumatic stress disorder as a result of the incident.
Martin Robertshaw, prosecuting, said her work had suffered due to her condition and she is still receiving counselling.
In a victim statement read to the court she said: “It was a perfect storm of awfulness.
“Even though the robbery only took a few minutes it has permeated every part of our lives and I cannot escape from it.”
Mahmood pleaded guilty to robbery and was jailed for six years, four months.
Mahboob, of Eden Mount, Kirkstall, was found guilty of robbery after a trail and sentenced to five a half years.
Mahmood, of Ash Grove, Hyde Park, was the subject of a community order at the time of the robbery for crashing his mother’s car into parked vehicles in the Hyde Park area.
Victoria Smith-Swaine, for Mahmood, said her client had been experiencing family problems at the time and had been abusing alcohol and drugs.
She said he carried out the robbery in order to pay debts of £1,000.
Mark McKone, for Mahboob, said the robbers did not realise a child was in the car when they set out to commit the offence.
Judge Simon Phillips, QC, said: “This incident has left the victim severely traumatised.
“It has had a profound effect on her emotional and mental state.”