It's the money adviser coming out in me, dealing with things like this is part of my job

I am not saying that it will work but it's worth a try, I would ask then for a full breakdown of the balance and then highlight all the charges "that were the vets fault" and then send this back to them with your complaint asking them to be removed.

If they won't do this you could try another angle, explain to them that due to their "error" the costs have increased to more than you budgeted for and you want time to pay in instalments you can afford