If I used my vehicle as a down payment on someone else's vehicle purchase, can I take it back if I have the title?

Your questions asks "if I have title," but then say you have no vehicle in a two car trade where she took the car "that is in her name"? Which is it is: do you have title or does she? If title to the car is in your name it is yours. If not the car is hers then you cannot take the car. However, if she is not making payments and you are making them because the car loan is secured by your car, you may be able to sue her for the money.