Thanks for all the advice!
Jamie's mum called at 9 o'clock and told Jamie to go home. The party ended at 4
There is a Dad in the picture, but he doesn't live with Jamie's mum and I've never seen him. Her boyfriend lives with her occasionally, though.
Jamie's grandmother lives nearby, and following your advice I am going to ask for her number today. I will also inform Jamie's mum that I *will* call her mother to fetch Jamie if she is left at my house without my consent again. You can believe that I was sorely tempted to call in reinforcements, but I didn't, for all the reasons mentioned.
We answered the phone because we live in a different country, and all our relatives were phoning DS to congratulate him on his birthday. If it wasn't for that, I would have turned off the phone. Not that it would have stopped Jamie's mum from sending her over anyway, imo.
Would it be polite enough if I say the following to Jamie's mum:
"Susan, I told that I wasn't able to look after Jamie and you abandoned her in front of my house anyway. It caused some disruption at the party, and I was left looking after your daughter for 5 hours after the party ended. I am going to need your mother's phone number so I can contact her to collect Jamie should this happen again. I am afraid that I would be forced to contact the authorities if I don't have contact details for family members."
I'm still spitting nails, I can hardly think of a polite way to tell her just how unacceptable her bahviour was. And I sill fell so unbearably sad for Jamie. She doesn't deserve to be treated like this by her mother!