This problem can be solved by hiring a professional who doesn't interact with the children to do the arguing, assuming there is enough money on the table to make that worthwhile.

(I mean, I agree it's a big problem. I also dislike haggling, and I think I would have done much better had i outsourced that function when I ran a business, even if I paid a lot to that person)

All that said, a sufficient guilt trip might be more effective than a fine in any case, and is something that a caretaker could probably provide.