License, registration, home, visiting.... oh my!

Generally, your DL has nothing to do with registration. For example, although Arizona is not our primary home/residence, we have a vehicle at our winter home. Arizona law specifically states that a vehicle remaining in the state 6 months and a day or more must be registered in AZ. If a vehicle is used and stored in multiple states less than 6 months in each, it would be possible to register elsewhere assuming a property address at that location.