As a LEO I can assure you there are plenty of people with more than 2 or 3 DUI's. It is not very hard for someone with an alcohol problem to get multiple DUI's and rack them up pretty quick.

The police start to recognize vehicles. Habitual offenders, be it domestic disputes or drunk driving or drug possession tend to become known.

And, as far as the firearm...legally it might be hers. Up until the police decide there's a reason to talk to him. The officers involved set the rules of the game long before the prosecutor, and their statements become reality. They can decide he was "in possession" of it because it was in the same room in a locked safe, or upstairs in an unlocked cabinet, or that he failed to cooperate. He's on the radar now, and it will come down to how reasonable the police he deals with are.