Be very very careful when you cancel a reservation --- it is best when you have a situation like this, to not just go ahead and cancel the guest's reservation on your own, but involve AIrbnb from the start, asking them for help. THat way, depending on what the family matter is, you may be able to avoid some of the penalties imposed on hosts for cancelling, or to keep some of the days open, as you are trying to do.
Call up Airbnb customer service for help. The Airbnb customer SErvice phone number for California is 1-855-424-7262 .