"I was frightened, but I was quite determined it was not going to stop me working," she says. "I knew what I was doing was right. I was not going to be frightened out of my school."
She was forced, however, to take extreme precautions until the threat of violence ended. Her daughter drove her to and from school, she was escorted to and from the car, and had to lock her office while inside it. Her state of siege lasted for several weeks.
At issue was the behaviour of the woman's little boy. Since arriving at the school, aged five, he had displayed behavioural problems, throwing tantrums in the classroom, grabbing other children and throwing chairs around. The school felt that he needed special help, which meant referral to an educational psychologist, but the mother would not hear of it.
Eventually, Mrs Mulholland decided that the disruption had become intolerable and that her school could no longer continue to teach the child. His mother was asked to take him home. At which point she let fly.
"She threatened to kill me," says Mrs Mulholland. The police were alerted, as were the local authority, Tower Hamlets, and the National Association of Head Teachers. The upshot was that the mother was banned from entering the school.
After a while the mother came round to the idea that her son should receive special help. He is expected to be the subject of a statement of special needs and to receive the attention of a member of staff recruited to take care of him in the afternoons.
The boy has become calmer, and the mother has made it up with the headteacher. "There is a good relationship between her and the school, in the best interests of the child," says Mrs Mulholland.
But it has been a searing experience for all concerned. The headteacher thinks that many parents are as needy as their children. Sometimes they require more help, because of the stresses of their daily lives as single parents on social security, or trying to combine single parenthood with a job. When their offspring get into trouble, it's the final straw. They regard any attempt by the school to sort the matter out as an attack on them as parents, and they react in unacceptable ways.
The Government's emphasis on parental rights has not helped schools.
"Yes, they have rights, but they have rights within certain boundaries," says Mrs Mulholland. "The whole social climate makes parents feel they can demand more."