She complained she had been treated unjustly and "victimised" by a teacher.
The teacher, meanwhile, said she was so shocked and upset after the row that her husband had to collect her from the primary school in Newham where she worked.
She said that all that prevented her from pressing charges of physical and verbal abuse against the mother was the guarantee the woman would be banned from the school.
"The experience of that day was horrendous. I would not wish this on any other colleagues and I expect to feel safe in my place of work."
The argument blew up at a sponsored sports event at the school. The mother's son was told that he could not collect an autograph from an Olympic athlete who was present.
The woman shouted at the teacher who then complained to her headteacher. A few days later Newham Council told the mother she would be prosecuted i she went beyond the school gates.
The pay-out follows a complaint made by the mother to Edward Osmotherly, the local government ombudsman. Neither the woman nor the school is named in his report, which was published this week.
The ombudsman's investigation looked only at the way Newham Council dealt with her after she was banned from the school. It did not consider the behaviour of the mother and the teacher.
Mr Osmotherly ruled the council was at fault because it did not give the mother proper advice on how to complain about the ban, keep proper records or act reasonably to ensure she received a hearing.
He recommended that the council pay the cash to the mother, who has had a previous complaint about teachers at the school upheld.
A council official said she was "the most difficult of parents the school had dealt with". He believed staff had shown "unparalleled resilience" in dealing with the case.
The ban was lifted around six months after the incident.