The easiest course of action is to rely on Airbnb - They are a 3rd party and make these situations easy to decide.
They will probably request a 100% refund.
Although incompetent, the guests did act in good faith: They intended to stay at your place. They came and tried to stay at your place, but were unable to (no blame to you). They paid money for a hotel.
This has happened to me before and I had refunded them.
Although annoying, this is the price of doing business.
To protect yourself from this in the future, consider making your Mother a co-host. Backup is always good.