As a co-signer on an auto loan, how can I go about obtaining the vehicle if the other person defaults?
Both of our names are on the title as well.
Unfortunately, co-signing the loan does not give you anything like the right to foreclose if the other person stops paying. To do that you would need a separate contract with the car's other owner, which I am presuming you don't have. Without paperwork, these are separate issues.
You need a lawyer. More accurately, you needed a lawyer before you co-signed the loan; there may not be much you can do now.