Driving Mexican plated car into USA

My husband and I both received our permanent residents visa and with the visas we are no longer permitted to drive our Tennessee/US plated car into Mexico. One scenario has us purchasing and registering a car from Zihuatanejo, driving that car all over Mexico and back home to the US in the spring and returning for the following season. Specifically are there problems we should consider crossing border going and coming. For example how long can car stay in US? I have added my email and can do a sit down here in Zihua or can phone you.