I've worked for barns from 5 horses to 70, and I've never seen anyone charge for an emergency situation like that. It kind of comes with the territory. I understand you are trying to run a business, but I think you need to take a close look at your pricing. There's nothing wrong with "nickle-and-diming" in theory, it's something I've looked into myself. The problem is that it results in a very rigid system and when presented with "gray area" situations like this, it tends to fall apart. If that's the way you want to do it, then you need to write out every concievable scenario
and put a price tag on it. Another problem is with a system like that, boarders may have a tendency to pick and choose what they want to pay for - one of the barns I worked at tried to put in blanketing policy, but it fell apart as many boarders would severely overblanket their horses but not sign up for blanketing, and the BO would remove the blankets to avoid a medical situation but couldn't demand a charge for the work (even if she paid me - she had to take the hit). The only options would have been to walk away and allow the situation to turn into heatstroke or worse, make blanketing/removal mandatory and part of the overall board agreement (include it in the total board price), or simply keep doing it for free.
That last scenario is why I don't like the "nickle-and-dime" structure. It's fine in a business that doesn't involve living animals but unless you're willing to walk away from a severe medical incident due to a boarder who won't want to pay (and I don't consider that an option, and frankly you may want to consider a non-animal involved business venture if you do), you're going to run into problems (you could do it for free, but lord help you if you charge another boarder down the road for the same thing...) If it is specifically in your board agreement with an estimated price figure (either hourly or other) then fine, but be very careful about coming up with random pricing to difficult scenarios.
What I would advise is that you look at your finances and how you've determined what to charge for boarding. I've always found boarding works best on a cost-based system, that is cover your costs first - and these costs must
be detailed, not just the fixed but the variable costs need to be estimated as well - , as well as your salary and profit margin, and factor in what is charged elsewhere in your area to come to what you charge for board. Things like broken fencing and emergency care factor in as a variable cost - do some homework, look at records, and figure out how much you're paying on average for these things - speak to other BOs and ask how much these things cost them each year. Just like you would set aside money for unexpected vet bills with one horse, you do this for a business as well. Factor an estimated sum for these variable costs and include them in your board - if there is a surplus at the end of the year, put it towards facility improvements, boarder credits, a fun event, whatever. If you've estimated far too much you can adjust accordingly, and if you've had a run of bad luck you're not completely screwed. The key is to cover all costs including your pay and startup debt without creating a price so high that nobody will board there. Unfortunately there is very very little profit in boarding, you are better off trying to break even with the board and hopefully take home a small profit, and making your living with lessons and training.
If this horse in particular is a constant problem then you need to have a sit down with the owner. A dangerous horse is a dangerous horse and your staff have the right to refuse to handle him - the owner can either train him, pay you or another trainer to train him, negotiate a way to keep him there with minimal handling and an action plan worked out in writing
as to what will be done in an emergency situation where he will need to be handled (IE you having authority to call in the vet and authorise treatment up to a certain amount, to agreed upon sum, etc in order to get the horse treated as quickly as possible to minimize handling), or she can find another place to board. In terms of property damage, horses break stuff. I only see it appropriate to charge a boarder for it if it becomes a chronic issue - IE a horse that is underworked/overgrained at the owner's insistence and destroying their stall, or any other issue where the horse is simply causing damage on such a routine basis that special (costly) preventative measures may need to be implemented to deal with that one horse.
Best of luck with your facility, boarding isn't for the faint of heart and as they say, if you want to make a million dollars with horses, start out with two million