That's a tough one.

I'd ring the vet and explain the situation and maybe they'll do the right thing and help out.

If it were me, I'd chuck the cat in the car, go to the vet's anyway and sit there with the cat until they helped

It's winter so your daughter might have picked up the sniffles from anywhere. I hope she gets better soon . It's been a dreadful season for colds and flu this year.

Does your neighbour know whose cat it is?