I have a daughter of the same age my advise to you is support the mother rather than disciplining the daughter. There are different ways of saying things. Instead of saying your daughter is a spoilt brat try telling your partner that you think she's a good mum and you don't think she deserves to be treated so babdly. Tell her that you can see she's hurt by her daughter's attitude and that you hope one day her daughter will show maturity and realise what a good mum she has. This way you are making your partner think about the situation without directly bad mouthing her daughter.