Struggling with our nine-year-old's behaviour and lack of support from partner

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I’m really struggling with our 9 year old daughter being rude, dismissive, hurtful, blaming, condescending, and excluding.
My partner normally resents me for being in any way critical of our daughter, and so effectively endorses or vindicates our her behaviour.
I feel intensely hurt by the combination, especially my partner’s lack of empathy. I don’t know how to change this pattern. I feel totally powerless.
Any suggestions gratefully received.
Thank you.

Your partner is the problem here - it's destabilising for children when parents aren't on the same page with discipline and undermine each other. This is something you need to sort out between yourselves so you can agree consequences and present a united front to your daughter. If you can't find a way to agree, maybe couples counselling would help?