Does the road being public mean that my family should have been forced to drive two cars, thus polluting more, all because of some people who can't stay out of other's business?

I understand the argument here, but I think it's bad. Government does get a say in what is driven on roads: safe cars that are often inspected and pose less danger to those around and inside them. That's already a lot of restriction, now we let the gov't pick favorites too? Government is not your fairy godmother, things you don't like will happen.

>my family should have been forced to drive two cars, thus polluting more, all because of some people who can't stay out of other's business

You're depicting one side of a question with a practical example ("more pollution") and the other side as though they are simply assholes ("they just can't stay out of other's business"). There is a reasonable version of both sides.

This is true, but someone else telling you how to live your life with obviously zero practical experience in how you live your life will generally seem unreasonable to you. My bias is showing, but my bias is, I think, reasonable.

The question didn't start with trying to take reasonable stock of both sides.

Weird question, but they probably do from time to time.

The question is implying if they use it on government funded roads, then the government should get a say on what is allowed.

This is silly reasoning. Of course the government has the authority to dictate their life, even if they didn’t drive in public roads. This doesn’t mean that it’s good for them to do so in this case.