If there are two names on the title, then a state can't register it in your name only , which is why the state didn't do if before. Your grandma need to sign the title over to you before that can happen. There is no notary needed in most states for this. Check with your state's BMV, or look online. Take your title with you when you go to negotiate the terms of the trade in on the car, and they will understand the situation. In most states you have 30 days to give them the title after a transaction.
Cant be done...if its registered in two names, both people must sign it. And they must sign in the presence of the notary. If one of them is deceased, a death certificate must be produced. Other than that, aint happening.