Mother-of-four Mary McCann, aged 35, was jailed for 49 months for killing her four-year-old daughter Lily and her 10-year-old son Smaller in the fatal collision on the M1.
She was also banned from the road for seven years and two weeks.
Aylesbury Crown Court was told Lily may have survived the crash if she had been strapped in, while Smaller - who died on his birthday - would certainly still be alive if he had a seatbelt on.
McCann had admitted two counts of causing death by careless driving while under the influence at a hearing in February.
She was on the way back from a birthday celebration as she drove the children in a white Vauxhall Astra northbound between Junctions 14 and 15 when it smashed into a Scania lorry near Milton Keynes, Bucks, just after 11pm on August 9 last year.
McCann had consumed at least 98 milligrams of alcohol per 100 millilitres in blood. The legal limit is 80 milligrams.
She was also speeding at at least 72 miles per hour on a stretch of motorway where the speed limit had been reduced to 60 miles per hour.
Lily and Smaller were pronounced dead at the scene.
Stephen Shay, prosecuting, said: “Shortly before the collision the lorry was in Lane One and the lorry was moving into Lane Two. The defendant was driving in Lane Two.
“For no obvious reason, the defendant drifted into Lane One. She steered right in an unsuccessful attempt to jump the lorry.
“The car sustained catastrophic damage to the rear side and rotated anticlockwise.
“Lily was ejected from the right of the car before it moved into the central reservation.
“The defendant said ‘God, why didn’t I put their seatbelts on?’
“Lily would not have been ejected from the car if she had been restrained, and she may have survived. Smaller would have remained in his seat if he had been restrained in the seat.
“His fatal injury was likely to have been caused by his head striking the damaged part of the car.”
Lorry diver Simon Denton told the court in a victim impact statement that the horror smash had left him suffering from nightmares and flashbacks.
He added: “This has left me depressed, anxious and in constant fear.
“I cannot go out and when I do I am looking behind me. I am scared.
“When she absconded I thought ‘why can you not stand up and take responsibility for what you have done?’”
McCann, from Derby, was taken to hospital to be treated for shock while another of her daughters, then aged two, was strapped into her seat and survived the fatal collision.
She also has a third daughter, then aged 13, who was not in the car.
Mr Denton was unhurt, but the motorway was shut for 12 hours following the crash.
McCann was arrested after she handed herself in to police following the smash.
She was bailed on August 24, but failed to appear in court in September last year when it was feared she had gone on the run and may have fled to Ireland.
Border Force was told to place alerts at all British ports and airports to stop her leaving the country.
She handed herself in later that month and has been remanded in custody since then.
On Monday, she sobbed from her cell at Bronzefield jail in Surrey as the case against her was read out.
Laban Leake, in mitigation, said the horror crash had been “unintentional”.
He added: “She has to be punished by this court and quite rightly so.
“However, it must be acknowledged that the true punishment for this offence, which was of course truly tragic, lies in her grief for her children.
“She has complex PTSD and a bereavement reaction condition.
“She was on psychotic medication, but she stopped it because she wishes to feel the blunt force of her grief.”
The court was told her surviving children are living with their grandmother and doing well, but they are expected to return to her when she is released from jail.
Sentencing McCann, Judge Francis Sheridan told her: “The driving in this case was not far short of dangerous driving.
“This is a heartbreaking case, to have to sentence a mother for killing two of her own children while drunk and driving as badly as you were.
“It is a disgrace that you drove whilst drunk with your two children in the back of the car.
“You will carry the costs of what you did for the rest of your life.”