A member of staff at the primary school called the police when the woman arrived stinking of alcohol.
Officers and social workers visited the mother-of-three at home later that day and found the children - aged three to seven - were missing and she was sprawled across the sofa.
She told police she had not been to collect the children and said they were still at school. She later admitted driving there after drinking a small amount of vodka but insisted she did not pick them up.
The children were soon found by the authorities at a local store, supervised only by a friend, aged 10. They were taken to their Coventry home before going to live with their grandmother.
Prosecutor Ian Ball said: "A breath test gave a reading of 110 compared to the legal alcohol limit of 35 and she later accepted she had drunk three-quarters of a bottle of vodka that day."
The mother, who cannot be named to protect the identity of the children, admitted driving with excess alcohol and child cruelty and was given a community sentence with two years supervision.
It includes a condition she take part in an alcohol treatment programme as well as an 8pm to 7am curfew. She was also banned from driving for two years.
Passing sentence at Leamington Spa Crown Court, Judge Richard Griffith-Jones told her:
You can't have another drink ever again. You have got to come to terms with that; it is poison to you and your children. I don't want to lecture you, but think about your children getting into your car with you in the state you were in. Can you imagine what could have happened?
David Rees, defending, said the mother's greatest fear was losing her children and that she would cooperate with any help she was given to tackle her alcohol problem.