This honestly seems like an awful way to be a host.
Your guest has problems so you say 'well here's the door buddy, if you leave, i'll refund you for the nights you don't stay, otherwise, shut up and deal with the problems and we wont pay you a dime'
I understand your perspective, because as a host you think 'oh well i dont owe him jack, if he leaves halfway through a stay, i dont even owe him a partial refund' which is TRUE, however, that is NOT how guests think.
Most guests think they are entitled to a refund if they leave early. I'm not defending their position, just saying I've encountered this a few times.
Your message should address this and be more tactful. This is what I would write:
"Hi *name*, I realize you're experiencing a sub-par experience with us, I've talked it over with my co-owner siblings and we've decided that in this case we want to make a special exception for you. We understand that you have been very frustrated by the issues you encountered. Since these issues are not typical of guests that stay with us, we wanted to offer you this: If you and your guests choose to leave later tonight (take all the time you need) we will refund you for the nights that you don't use on your booking. If you choose to stay with us in spite of the problems, please understand we cannot offer a refund as our cancellation policy does not allow us to. However we would be able to *INSERT FIX HERE (such as sending handyman, etc.)* in the morning. If we are unable to address all your concerns we would be able to offer you compensation of $XXX for the inconvenience. I wish there was more we could do, but as airbnb hosts our tools are limited in what we can offer guests who experience problems. It is clear our past guests damaged X, Y, Z and we apologize that we did not catch it in time to fix it for you. I will be discussing this with our cleaners once you leave so we can better handle future problems for guests and ensure this never happens again."
Writing more shows we care as hosts, it shows we put in effort and thought about this long and hard. Writing that we will prevent this in the future makes guests feel like they don't have to leave a bad review, because we've fixed the problem already. Giving them a few options gives the guests a feeling that they are in control and determine the outcome. Writing that we are limited by our cancellation policy puts the onus on the rules in place by our business, not our personal opinion so they won't argue with us. etc. etc.
Just my 2 cents on how I handle stuff.