The guest is bang out of order. Of course they planned for her to stay and lied to you when you stopped by.
I would express your disappointment at her response and point out your house rules (presumably) say that only those who have booked and paid can stay.
Point out they must have arranged in advance for her daughter to camp out or they wouldn't have brought their camping equipment from the land they were staying at.
And that they have put your property at risk as if there had been any damage you wouldn't be covered by your insurance .
I would call Airbnb to flag this with them and emphasise guest has implied a negative review because you asked them to pay for additional guests not listed on the booking.
I would leave an honest review and Pursue payment - they are not going to give you a positive review now anyway.