You have asked for advice concerning a specific legal scenario, so if anyone on the Forum responds with specific advice regarding this specific legal scenario, then they are providing legal advice, for which they must be an attorney at the bar in the state of Nebraska.
I'm responding here in a more general manner and not to the specific situations that you have presented. 'Cuz.........I'm not an attorney at the bar in Nebraska.
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1. A handgun registered with a municipality clearly indicates the identity of the ownership of that handgun. Any owner of a handgun who holds a CHP in Nebraska is exempted from any and all municipal codes requiring handgun registration. So wherever that handgun might be located in Nebraska, it is still exempt from municipal registration. All handguns of a CHP holder are likewise exempt.
2. Generally, any otherwise legal, unloaded handgun that is locked in a vehicle in a location which is not accessible from the passenger compartment is not in violation of federal or state law. Glove compartment, console, door compartments, under the seat, under a seat cushion, carry in a purse or on the body, or anywhere else in the passenger compartment would be concealed carry and legal only for a person holding a concealed carry permit. Placing the unloaded handgun in a locked case in the trunk of the automobile is the best practice for legal automobile transportation.
3. Unloaded, cased firearms carried in the trunk of an automobile operated by a non-CHP driver do not have to be declared to law enforcement officers during a traffic stop.
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Sorry that I couldn't address your specific questions with specific advice. But that's the way it is.
FWIW, The Nebraska State Patrol recommends that persons desiring specific legal advice seek out an attorney who is knowledgeable with respect to Nebraska firearms laws.