We plan to move to Mexico in May. My auto license plates expire in Jan. and I have an option to renew them for either 1 year or 2 years and they are kind of expensive. How long will I be able to drive in Mexico with my auto plates?
Will your resident status be as tourists, temporary residents, or permanent residents? And, where do you plan to be while in Mexico? When you enter Mexico with your car, if you're only going to areas in the "free zone" (Baja California, Baja California Sur, and the northwest part of Sonora), you don't need a Temporary Import Permit (TIP). If you're going anywhere else in Mexico you will need a TIP. I believe you can get it for up to 180 days (which would match up with a tourist visa), but I'm not completely sure about that. I live in Baja California Sur, which doesn't require a TIP. If you are a permanent resident, you would need to import your vehicle, the temporary import is not an option.
This website has a good overview of the details of importing and driving a car in Mexico: https://yucalandia.com/driving-in-mexico-issues-fun/importing-driving-a-car-in-mexico/
I can't really comment on how long you can drive your car in Mexico with expired tags. If your plan is to live in Mexico for an extended period of time, then you may want to import it, or purchase a vehicle in Mexico. Another option that many expats from the United States use is to register their cars in South Dakota because that state doesn't require residency and you can handle the renewal process by phone/mail.
FYI, if you are planning on temporary or permanent resident status, you will need to start that process in your home country at a Mexican consulate. Again, more good info at the Yucalandia site: https://yucalandia.com/answers-to-common-questions/new-rules-and-procedures-for-immigration-visiting-and-staying-in-mexico/
Enjoy your time in Mexico!