Maybe go with her, and stay for the whole thing. When she shows signs that she is ready to go home then leave together and talk about the experience. Did she end up enjoying it in the end or did she genuinely not want to be there. You can treat it as “we have been invited to xxx house, mummy will be there and we can leave whenever or after one hour.”
Use this as an opportunity to understand why she might behave like this.
my DD had selective mutism, didn’t speak to anyone!! Spoke to the whole family (my guess is all the suppressed conversations came out). I remember being so frustrated and wondering why she didn’t even want to say hello to a friend at school or my friends who she would adore, speak to non verbally but refused to talk.
I later noticed that her body was having a nervous reaction everytime she was asked to speak. She would play with her hands, go funny. It’s like she wanted to speak but physically couldn’t. And I worked with that and we kept on working towards the anxiety behind it.
She is a tween now and to this day, before she goes to someone’s house, if she isn’t comfortable, I make sure we are there together first. If I can trust the family and if she is happy to go there, I then drop her, stay for 30 minutes then leave etc until I can trust the other family.
Good luck x