The other part of your question as I understood it dealt with buying a firearm prohibited in NY and keeping it in your other home. If it's not in NY, their law doesn't apply at all. Welcome to freedom.
Don't forget that it is legal to purchase and receive a rifle and shotgun from an FFL outside of your state of residence. As a WA resident, I could purchase and take possession of a rifle or shotgun from an FFL in Montana, for example. HOWEVER, if I am purchasing a rifle or shotgun from an FFL outside of my state of residence, Federal law requires that both the laws of the state the FFL is in, and the laws of my state of residence both apply and must be met.
So, if a New York resident travels to Nevada for a vacation or hunting trip, with no intention of making a home in Nevada, it would be illegal for them to purchase a rifle or shotgun that they could not legally possess in New York.
If they were going to live in Nevada, say for the winter and then return to New York for the summer, then it would be perfectly legal for them to purchase an evil AR-15 in Nevada that would be illegal to possess in New York - but in order to do so they would have to prove Nevada residency to the FFL. Of course, the evil AR-15 would still be illegal to take back into New York, at least without doing whatever New York law would require to make it legal.
So, commander which state are you the legal resident, would go by your voter rights would it not.
As was stated earlier, voter registration does not establish residency for the purposes of firearms transactions. Neither does a driver's license or paying taxes. The only thing that establishes residency, in Federal Law, for firearms transactions is presence in a state with the intention of making a home there. PERIOD. Voter registration, paying taxes and a driver's license may be used to prove residency to an FFL, but they do not establish residency.
For example, I have held a Wyoming driver's license for 30 years. I have been registered to vote in Wyoming. I pay state taxes to Wyoming (which is zero, because they don't have a state tax). But, for the purposes of firearms transactions, I have not been a resident of Wyoming since 1988 when I left Wyoming to join the Navy. I have been a resident wherever the Navy has ordered me to, and/or wherever I sleep at night. On one set of orders, I was a resident of two states simultaneously. I had permanent duty orders to Connecticut, which made me a resident of Connecticut for the purposes of firearms transactions, but my house was in Massachusetts and I commuted every day, so I was also a resident of Massachusetts for the purposes of firearms transactions, and could legally do firearms transactions in both states - but not in Wyoming.