Are police of a small town legally allowed to arrest you for curfew when you are in a car driven by an adult who is not your parent and you are under the age of 18?

Probably. Most curfew laws specify that you must be accompanied by a parent or guardian so kids can't hang out with older kids and be legal.

A curfew law that allowed an 18 year old to run a gang of 16 year old kids would be pretty useless to everyone concerned.

There are no 'small town' laws. Police officers carry the same authority regardless of which city employs them, and they are bound by the same regulations.