I concur with @JohnnyB . This is a total non-issue as you're maintaining both as residences. Buy 5 more and you'll get the same answer Both residences are where you'll be residing, so BOTH are EXEMPT LOCATIONS.
@lhrocker So now we "pull teeth" to get the full story:
Are both houses in the same town being used as YOUR residence OR is your intention to rent the old house to someone and transfer all your worldly possessions, including your firearms, to the "new house"? If you're moving out of the old house, and changing your driver's license, you'll need to get a new Yellow Card.
Even if you rent it out, it's still property YOU OWN, so you're allowed to patrol it armed. Hair-splitting is a specialty of mine, so...
You can own many houses (or vacant lots) in NJ's 21 counties, and carry or store firearms at any of them, provided they are secured and away from prying hands...OR transport any number of firearms TO them at any time day or night. I've written about this several times in the past.