Fan site about the special...worth checking out for more details on the subject.
Imagine a mechanic telling his brother-in-law "pay me for parts and labor, or just take it to the dealership". I can't imagine this. At the very best, I can imagine the mechanic saying "XYZ is probably wrong, I don't have the time to fix it, take it to RST and tell them ABC. They should be able to fix it for $HIJ"
It doesn't have to be a moral hazard. Chances are, you will charge your family less than what they would pay at a shop. You probably also have better availability, and more liability (since I'm assuming if you do a bad job, you'll suffer a lot more than a stranger at a shop would).
I know many people would argue that its immoral to charge family for tech services, given that they've probably helped you, y'know, grow up safely and possibly even helped you develop those skills. But these are intangible things that shouldn't be measured or compared in the first place.
What seems evident about the original poster is that his family doesn't seem to value the work he does, since they proceed right ahead into undoing it immediately after he fixes it. If I were a mechanic who fixed cars for my family members at a discounted rate, I would probably be within my moral rights to threaten ceasing the discounts if it became apparent that they were abusing the car I was fixing and then bringing it right back to me. Clearly, they aren't being considerate of my time and skills, and asking them to consider compensating me financially can be a polite way of enlightening them on this matter.
I know a lot of people have a hard time mustering up the courage to tell their folks to pay up, but take my advise - you're doing them a favor in the end (not to mention giving them a lesson the value of what you do).
Neutrinos have bad breadth.