CCTV footage played at Derby Crown Court showed Gelu Rus first swerve left, then right, then left again and collide with a Nissan Qasqai containing the victim, her 90-year-old husband and two of their children.
That car, which was being driven by a daughter of Elizabeth Harrison, was forced off the southbound carriageway, up a bank and into a tree.
Mrs Harrison, who was described as “busy and active” suffered multiple fractures in the crash and died two days later in hospital.
Her husband Roy, who also suffered broken bones in the accident survived, but tragically he died from an illness almost a year to the day after the collision.
The crash caused miles of tailbacks on the southbound carriageway of the motorway at the time with drivers delayed by hours and diversions put in place.
Now Rus, a father-of-two, has been jailed for 10 months after admitting being responsible for the death of Mrs Harrison.
Judge John Burgess said: “You cannot listen to a case like this without feeling how unfair life can be sometimes.
“A much-loved woman of 86 lost her life and her 90-year-old husband was seriously injured.
“He lost his wife and his daughters lost their mother.
“On the other hand none of this was the intention of the defendant.
“He was keeping to the speed limit, he was not seen to be driving in a way that suggested he was going to take any risks.
“There are occasions when people behave appallingly, even wickedly and the consequences are small or even negligible.
“Then there are cases where the blame attached to the person may be small but the consequences of their actions are devastating.
“Mr Rus said that he believed he fell asleep at the wheel of his car.
“He had been up early that morning and he had been to work.
“He only had five hours sleep and the heating in his car was on full.
“He said he believed this led to him momentarily closing his eyes and falling asleep.”
Mark Achurch, prosecuting, said the crash happened on the southbound M1 between junction 29, for Chesterfield and junction 28, for Alfreton, in the early afternoon of December 30, 2017.
He said Mrs Harrison, of Roper Lane, Barnsley, was sat in a rear passenger seat of the Nissan Qashqai being driven by one of her daughters.
Another daughter was in the front passenger seat and Mr Harrison, who was 90 at the time, was sat in the back alongside his wife.
Mr Achurch showed CCTV footage of the collision to the court.
It showed Rus’s blue Saab 93 in lane two approach the Nissan which was in lane one.
Mr Achurch said: “An independent witness, who was behind both vehicles, saw the defedant’s car swerve to the left and into lane one and then to the right into lane three narrowly avoiding another car.
“He then appears to over compensate and swerves back left, colliding with the Nissan and pushing it off the carriageway.
“The Nissan goes up a bank and into a tree before beginning to roll back to lane one.”
Mr Achurch said Mrs Harrison was found to have moved forwards and into the footwell of the rear passenger seat in front of her.
She was airlifted to Sheffield Northern General Hospital but died on January 1.
He said a post mortem examination revealed she had suffered multiple fractures to her ribs and a fractured femur.
Mr Achurch said subsequence investigations showed there were no defects with with the car, there no evidence of speeding, alcohol or drug use and that Mr Rus was not using his obile phone at the time of the crash.
He said: “He was interviewed and told officers his wife and children were in his car and that he had no idea why the collision occurred.”
Rus, of Laurie Avenue, Forest Fields, Nottingham, initially denied being responsible for the accident but later pleaded guilty to causing death by careless driving.
Mr Achurch said he is currently a banned driver having amassed 12 points on his licence for speeding offences and for driving while using a mobile phone.
Chris Hallas, for Rus, said at the time of the crash his client was on his way home to Nottingham after dropping his mother-in-law off at Doncaster Airport and “made a mistake” in driving as he did not want to let her down.
He read out part of a letter Rus had written to the judge,
In it he said: “I know I am guilty and I am so sorry.
“I could not tell the truth at that (earlier) hearing because I was in shock.
“But I am glad I can tell the truth now.”
Mr Hallas said: “He is a family-orientated man who has a wife and two children, aged five and two, who were also involved in the crash.
“He came here in 2014 from Romania for a better life and his life revolves around the church.”
As well as the jail term, Judge Burgess disqualified Rus from driving for two years and five months.