Real-Life Decision Making -- Solution
You wait and see if the family wants to pay the extra money.
Doing this means they will have to wait until at least Monday at noon before their RV is ready. This is if they choose to have their RV repaired at your shop. Any way you do it, they will be delayed. This will foul up the travel arrangements.
When you tell them, they are very upset. They fully expected to pick up a repaired RV. The person they plan to meet is already on the road and cannot be reached. They ask if any other shops are open. The best you can do is help them find a place that can fix the problem as fast as possible.
This option, though sparing them from a surprisingly larger bill, leaves them no further ahead than when they arrived. Besides the frustration at the delay, they have to put up with a whole wasted day.
As for you, even though you could not have prevented such an honest mistake, you still will appear incompetent and unprofessional.
Steve Wallace is a customer service rep. He has to look into his crystal ball on occasion. "Sometimes a business customer is in the middle of a big project when their computer fries. They cannot stop for a moment. They just want it fixed, period. I have to find a way to make the repairs that work and don't break the bank."