BIL's DP has a DD aged four. She's a nightmare; stroppy, whinges constantly, loses her temper when not getting her own way. Some of it normal for her age, but she's noticeably more difficult than any child I've known at that age. No discipline from her mum, even when she has hit my dcs, broken things etc.
A few weeks ago we invited BIL and his partner for dinner. Evening invitation, didn't mention the child. Our DCs were staying with grandparents. When they arrived, the little girl was with them, in her PJs. Crossed wires possibly, but they were obviously hoping she would end up staying over. She ran riot and unchecked throughout the house for hours. She then through a tantrum as she was leaving and deliberately kicked my dog in the face. I shouted, in shock more than anything, her mum just told her that was unkind and to apologise to the dog 
they left soon afterwards.
I was furious! Thankfully the dog is as soft as they come and just wandered off to bed looking confused, but that is pure luck and there are no guarantees she couldn't snap. Had she bitten this girl I have no doubt they'd have demanded she was PTS, and I'd have been forced to rehome her. DP and I agreed that we would not have them over again unless things improved with her behaviour.
Since this, MIL has invited them to join us on Christmas Day without asking me first. They are all basically making out that it's me being precious over the dog rather than taking any responsibility for her behaviour, and suggested I send the dog to my mums "if that's the issue". It isn't!! I sense a big family fall out will ensue but just wanted to check whether IABU before making a fuss!