I've known this school mum for years. We've always been polite and said hello, but not friends as such. She is known to be a tiger mum, ie very protective of her children (now 16 and 13).
Her younger one is now in my daughter's class in high school, and they have struck up a close friendship. Occasionally, our daughters have got into a bit of trouble at school. Honestly, nothing major. They are at a fairly strict private school and their behaviour is relatively good. They might hide out in the bathroom during break if the weather is particularly cold outside, for example. They do their work, no backchat to teachers, no bullying, etc.
Recently my daughter has come home saying that the mother of her friend has told her daughter that she doesn't like my girl, that's she's a bad influence. Friend has told my daughter all of this. I feel really disappointed at this. I have been making her daughter feel welcome at my house, having her for dinner and sleepovers. She never has my daughter over, but funnily enough, seems happy to accept my hospitality towards her daughter 
I'll say one thing for my daughter, she is polite and respectful in other people's houses, and people often comment on it.
My daughter has just asked if this friend can stay over tonight, and it sticks in my throat to be honest.
It just seems hypocritical and two-faced of the mother.
AIBU?