With countless thousands of cars and even more people visiting inside Mexico, one might get the impression that someone, or maybe even a couple, or a whole family group would be required to go back home and leave their vehicles behind for a time before they came back for it. Whatever the reason for leaving Mexico for a short time- no one asks why.
You board your plane, give up your FMM paid-up tourist cards and fly back. You both can go if you need to, why not if your car is secured? The TIP for your car is tied to a passport and control is through the Aduana, or Customs. Your FMM is provided by Imigracion. You will likely get another as you return before you leave the plane, usually included in the price of your ticket. This second FMM should give you all the time you need to continue in the country. Stop at the border as you exit Mexico and turn in your TIP for your deposit. And your second FMM's if you won't be using them again soon.