No at 7.5 I would not be letting my child stay at someone's house I don't know. Simple as that really.

I would let her go to the play centre and then make some excuse to the parents about having other plans etc etc. And as for DD, you are the parent and in charge so I would simply explain your reasons to her and tell her that when you know the family more then perhaps you could arrange a sleepover.

Don't mean to sound harsh but thats the way it is