@Ayesha-and-Tom0
Ayesha, don't cancel, simple as that! The long term ramifications from cancelling will far outway any benefit! Guests tend to avoid hosts who cancel and that cancellation posting will stay on your review page forever.
What you are talking about does not fall under the extenuating circumstances umbrella....you are simply double booked and that is it!
Now what you have here is a damage minimisation problem....what is going to affect you least in the long term!
Firstly, although your guest has stated the booking is to remain firm it may be worth trying to make them an offer they can't refuse....explain again the situation and offer them a special price of say 50% if they would be prepared to bend a bit on their dates.
It is amazing what a substantial discount does to people, and I know, it costs but, that cost is the lesser of the evils here!
If they still stand firm and will not budge, say OK, it is going to be squeezy but as a host cancellation is not an option we will do it and do our best to make you welcome.
Now this will do one of two things...it will force them to cancel because the situation is unacceptable to them, or they will come regardless but give you a caning in the review process....and frankly Ayesha and Tom, I think that would be the preferable path.
Remember as long as you tell ABB that you are not prepared to cancel for any reason on your end, they will not penalise you, they may think is isn't quite right but they won't penalise you!
Secondly, are the friends willing to be flexible on dates, could some compromise be reached that would allow your friends to come at a time that fits in with your booking.
Without knowing more details of the situation....the length of stay.....amount of room available these are the only suggestions I can offer!
Hope you can sort it out.
Cheers.....Rob