Per Airbnb Policy: In general, cancellations and refunds for Airbnb reservations are governed by the listing’s cancellation policy. In the rare circumstances that large-scale events prevent or legally prohibit completion of a reservation, the Major Disruptive Events Policy (the “Policy”) may apply. Unfortunately, passings of family are no longer considered extenuating circumstances so therefore the listings specific cancellation policy remains in place.
That being said, you can contact the host (which it sounds like you have) and they can agree if they want to refund you outside their policy. Most hosts will not cancel from their end as they will be penalized. They will likely request you to make the cancellation. As someone else mentioned, if you are planning to rebook, you can also request a reservation alteration and try to reschedule for a different set of dates. The host will have to approve this though.
Given that you were so close to the reservation date when the incident occurred, that host lost an ability to rebook those dates. While I sympathize with your situation, and know passings are unexpected, for a lot of host Airbnb is their livelihood and way to support themselves. By refunding you they are essentially losing income.
My suggestion would be to come to an agreement regarding rebooking since this is already something it appears you talked about. Be clear on the amount that is to be refunded. I would ask the host, "if I rebook can I expect to be refunded for the original reservation in the amount of X within 24 hrs. " If they agree, make the reservation and then see if the refund is processed. If not, you are allotted 48 hrs. to cancel penalty free if the reservation is 14 days out. This way the host is offered security in the rebooking, and you are offered flexibility in cancelling in the event the refund agreed upon is not honored.