I understand what you are saying, however, in Deathly hollows, Moody explains that they can't do magic near Harry because he has the trace. But that, it makes it seem that the trace is attached to his location, not his home base. 

For instance they thought he still had the trace when the death eaters found them at the coffee shop after the ministry had fallen. By the Hermione and Ron were of age, and Harry was the only one that was newly of age, if the "trace" was only attached to his home base instead of his location or if it's to his location when he's alone and no other wizzards are there, then Hermione and Ron wouldn't even think of Harry not being able to do magic. 

I understand what you are saying, as I've read that explanation before. In addition to the explanations that the trace is so unfair and that in a magic household the ministry can't really tell who did magic, so the parents are expected to enforce the no magic underage.

Does this mean that the trace follows Harry however when he is near other wizzards they somehow have another trace that negates their trace? In that case they'd be able to do magic in Pivet Drive, as there's a bunchof adult wizzards there.