If the parent gets offended and can't accept the no, or even take the hint, she's likely the reason why the child is so annoying!
Exactly.
There was one girl at school, M, I used to have a love hate relationship with, eventually she left me alone. I'd be friendly but then she would be all intense and needy and always have to sit next to me, and she copied my work, which made me really worried I'd get into trouble- if we both handed in the same incorrect answers!
Her mum was a bloody nightmare, just really jealous, competitive and weird. Accused me of bullying her daughter, shouted at me in the playground in the morning (when I was about 7 years old), badmouthed me to other parents- we both went to the same dance lessons too (and I was further on than her daughter which mum couldn't stand) and she confronted my very mild-mannered dad, who really lost his temper with her. I had been for one playdate round there (before it all came to a head) and felt really uncomfortable. Her mum was just firing questions at me about all sorts. I think she thought she ought to be queen bee or something as her husband was a local councillor.
Looking back (40 years ago now!) I feel a bit sorry for M. Her mum was terribly insecure and nasty, goodness knows what went on at home when I wasn't there.
In short - don't make her go.