How awful @Stephanie1584
What sort of damage did they actually cause and what sort of costs were involved.
Sorry it's not clear from your post on what grounds did Airbnb turn down your claim?
I hope you reported the guest to the police for criminal negligence and the woman to social service for leaving children without adult care.
In your situation I would pay to take Airbnb to arbitration. It does have a small costs which they need to cover if you win.
I would also approach my local media about the story....bet Airbnb will change their tune when approached by a journalist.