Establishing residency

I can tell you about TX and you will have to check with Wyoming.
TX bases your residence on your last known address. We also sold our house.

For your car registration, contact the Vehicle Registration office, you should be able to leave your old address on for residency purposes and you add a U.S. mailing address to your parents' house in Utah. Same for your insurance on the car. That way you maintain your connection to Wyoming if that is where you want your residency. Your voter's registration also is based on your last known residence and you give them a Mailing address that will be your parent's house for your voter's ID cards. Same with your driver's license. TX told us since we were moving out of the U.S., the address on our driver's license remained our old address with a mailing address to parents' house in OK for renewal notices.

I visited all the offices and told them we were moving out of the U.S. They told me how to handle each one, some I handled right then. Even though we own a home once again in TX, our U.S. mailing address is still my parents in OK, because no one there to pick up the mail in TX.

It does not work that way in other states. To renew a DL you need proof of current address. The address on utility bills, mortgage statements (there is a list of acceptable documents) must be in the state you want the DL. For the car, it might be better to just rent a car depending on how long you are in the U.S., you can get nonowners insurance cheaply that allows you to drive a rental but this will depend whether or not the other car is insured. To renew registration and go through all the hassle for a short time, rental cars are sometimes a better option.