I'm sorry you are in this situation. It is so kind of you to offer a home to your nephew and his family.
Why not ask your nephew or his parents to cover the cancellation charges you have had imposed on you as a result of making your listing available to your nephew and his family @Brian2283 This is the best way to cover the £200. They are benefitting from you being so generous, so it makes sense that they cover the cancellation fees.
I can't see how you can appeal against the cancellation charges, as they have been rightly applied as your cancellation doesn't meet Airbnb's EC policy for host cancellations.