It's going to be difficult to find a lender that is going to be willing to roll a lot of negative equity into a new loan. Given the fact that you claim not to have high scores you are probably looking at an extreme interest rate anyway.
As far as "your" car in your dad's name, you can use it as a trade in if he signs the title to the dealership or to you. He is the only one who can transfer ownership at this time.
I am not real worried about the "negative equity". The trade in value would be pretty close to what is left on the loan, so I shouldn't be too bad off there. I just have one of those bad "gut feelings" about it that makes me want to get rid of it. I have had a couple things fixed on it lately and I just have this feeling that there is going to be more to come--nothing really that is going to negatively affect its value now, though.
My main issue is that I didn't know how it would work signing the title over to the dealer with the bank lien on it. Can what left on "his" loan (minus trade in value), be rolled into my loan. I actually don't think there would be much left over to pay since, like I said, the trade in value is pretty close what is still owed.
Sorry, you asked about rolling over the loan from the current car into the new call. By all definitions that is negative equity. However, I assume that you are prepared to take care of that in a cash down payment.