My girlfriend recently financed a car as the primary holder and her mother cosigned it, with that it was promised (verbally) that the car was going to be for either my girlfriend or her sister. After said contract was signed for and down payment was given, her mother tells her that the car is actually for the mothers boyfriend. We wanted to know if we have the power to take the car and if need be. in a legal case take action to keeping the car. The car is still in the lot and the title is in my girlfriends name.
Laws vary by country/region, but typically the title dictates who owns the car. A co-signer is lending their good name/credit score to help secure financing. They are obligated to pay but generally have no ownership rights unless they are also on the title.
This is true in Texas, a co-signer has no legal rights to the car. So, if your girlfriend is the only name on the title she can do with it as she see's fit.
You'll find many questions about co-signing where the overwhelming opinion is that you really shouldn't do it unless you are willing/able to basically buy the thing for the person you're co-signing for.