I cosigned a loan for a vehicle and the person is not making payments. Can I get the car back from that person?

Not unless you are on the title or registration.

Unless you have a contract which allows you to take possession of the vehicle in this situation (which I very much doubt since the lender would never have allowed it), no.  You can sue the defaulting party for any damages you suffer from their failure to make the payments (i.e. the money you have to pay the lender as a cosigner on the loan) and, if you win, obtain a judgment.  If you obtain a judgment and the debtor doesn't pay it, you can follow collection procedures, including causing the car to be sold to pay the judgment, and, if you are the high bidder at the sale, you can be the buyer without paying any cash, just having your bid deducted from your judgment.