A cosigner, or co-maker, of a note has the full rights and responsibilities of the signer or maker. Basically they are stating that when the signer doesn't pay, they will pay. Because the lender is using the cosigner as the debtor, the cosigner can enforce the note as well.
The question is can they take the car back. Even if your parents are holding the title, with your name being on the title, you would have to sign if they wanted to sell the car. Likewise, you cannot sell the car unless your father signs.
As a corollary, if they do take the car back, you will still be responsible for the payments. If you stop paying then they will be liable.
Your best option is to try to arrange a solution with your parents. If that doesn't work, then you may need to find a way to transfer your interests in the note to your parents for the payments you have made this far.
The answer has nothing to due with whether or not they have guaranteed (pay if you don't) and/or cosigned (obligated as you are) a loan for the vehicle. The question is about ownership and then, maybe, control. First, the title holder can do what they want so long as it doesn't divest another owner. Your parents can exercise control over the car, but not to your exclusion if they are on the title. If not on the title, perhaps they have some type of agreement with you that if you don't pay and they cover a payment, they get the car. In this situation, if they can prove it, then yes they can exercise control over the car. However, unless someone has a power of attorney that I am unaware of, the fact of the matter is that neither can legally divest the other of ownership with the consent of the other or as a result of Court order.
So, assuming there is not agreement to take back the car, you father cannot divest you of ownership nor exclude you from the car. However, this isn't a legal question. The amount at issue isn't that great I would assume, if your father is taking the car back and excluding you then you have a good case for sticking him with the debt (not that you don't owe the bank, but that you would probably be able to force him to cover your part).
No,this isn't a legal question worth an attorney, it is a common sense question. From your father's perspective, getting married has nothing to do with the debt as marriage in now way effects his ownership in the car. What he should be thinking is that you are already being punished enough by getting married. As a result, he should have your back. Conversely, you have to ask yourself whether you wife is hotter than the car!!!!! Funny, I know. But seriously, don't worry about the car. Your future wife is worth the risk or she shouldn't be your future wife. Incidentally, since you are getting married, it may be strategically beneficial that you call you dad's bluff, but only if there isn't room in vehicle for kids. Indeed, call the bluff, have him take the car back, sue him to buy you out due to his unauthorized exclusion and control. Start World War III over this marriage. Your wife will love that!