By the way, there's another case, U.S. v. Jackson which analyzes Florida law (which is very similar to Virginia law in this respect) with respect to the "violence" thing in a slightly different context (enhanced sentencing). That U.S. Sup. Ct. case used pretty much the same analysis as was used in White.
The reason cops can arrest people who are not actually guilty of crimes is that they don't need to know or care whether the arrestee is actually guilty. All they need is probable cause to believe that a crime has been committed and that the arrestee is the person responsible. If the guy's got a gun, and they know he's been convicted of a domestic assault charge, they'll argue that's probable cause. Wrong, of course, but it's good enough to survive their "qualified immunity" in a civil case, since they'll argue that they were reasonable cops doing their job and reasonably believed that "domestic assault" was a "misdemeanor crime of domestic violence". That's enough to at least shoehorn seizure of the arrestee's firearms. And God help the man who attempts to buy a gun from a dealer, and, filling out the forms, truthfully checks the box, "NO", in response to "have you ever been convicted of a misdemeanor crime of domestic violence", and signs his name under penalty of perjury. That guy will probably be "delayed" to give the VSP time to get to the shop to haul him away. That's why I recommend a pre-emptive strike in the form of a declaratory judgment action. Expensive, but better than some of the alternatives.
To answer the other part of the question: Under the U.S. Constitution, the United States is completely lacking in "the police power", which is reserved exclusively to the states. Since the invention of the FBI, which was supposed to have been limited to "investigations" in support of the states' law enforcement, the U.S. has been (unlawfully) getting more and more involved in police work, and there are federal agencies that actually believe they are law enforcement agencies are funded as such and behave as such. However, the Constitution intentionally limits the power of the U.S. by making it dependent on the states for enforcement of its laws. All persons acting under the law enforcement authority of a state government are empowered to enforce U.S. law within their jurisdiction.
Implication: that Sheriff in Arizona or some such place who keeps enforcing federal immigration law is the only person in the U.S. who's acting lawfully within his authority on that issue. The authority and power of the U.S. is to stop people at the border.