The requirement for Penny to join Girl's Night is 25 friendship and less than 5 rivalry- which pretty much means you cannot have any rivalry with her.
That might be the reason then. But there is still the matter of not receiving any refusal from Gisette
that's really strange, on first look I don't see any bugs with Gisette's invitation/response and wasn't able to reproduce it, sorry <3 Is anyone else having the same problem?