Oh dear what a horrible situation. @Heike226
Why did you let the guest stay when you knew it was a third party booking? @Heike226
Why have Airbnb blocked out dates on your calendar.
What did the son say when you raised these issues with him?
Presumably you spoke to the mother who is staying about her defecating in communal areas and the state of her room and things haven't improved (hopefully you followed this up in writing). Does the mother have health issues which are leading to this behaviour.
Unfortunately because you accepted a third party booking Airbnb don't have to help you in this situation.
All you can do is tell Airbnb they need to cancel the booking as it is a third party booking and the person who arrived is not keeping communal areas clean and is upsetting other guests. Once they cancel ask the son to come and collect her.