Car finance dept screwed up what can i do?

My husband and I purchased a vehicle on 7/22/2015. I traded in a 2012 Mazda 3 and we purchased a 2013 Honda Pilot. We signed all the paperwork and gave a 500.00 down payment. While there we discussed if we could transfer the tag off of my Mazda since it was in only 1 of our names and the new one is in both or off a vehicle we had at home that we were also selling. The finance guy said he did not know to just let him know and he would do either one/ We then left. A few days later the bank calls to verify everything and also stated the GAP contract was incorrect. They had charged us too much so it would have to be resigned. I told her that we were 2.5 hrs from dealership it is near Charlotte NC and we're in SC. She said not a problem they could mail to us. She told me to call the dealer and arrange for them to mail. I called and spoke with Paul and he told me no problem to mail and also updated him on the tag info that I wanted them to transfer the tag we had at home on the other vehicle. He had me fax the registration of the one we wanted to transfer.

So… Waited and waited called back several times and was only put through to voicemail and as of today the loan has still not been financed.
I did speak with Jeff and Jessica on 8/21 because I still had not heard anything or gotten anything to sign and no sign of new registration. Jeff stated he did not know who dropped the ball but would take care of it. While on the phone I realized he was the same guy that messed up the original paperwork. So I ended up getting very frustrated with him and hung up. I called back and spoke with Jessica and she infomed me they would overnight the paperowrk that I needed to sign and she assured me that she would have a manager contact me. After that I called the original bank back and asked where the deal was on there end and was informed they had sent everything back to the dealership because they were no longer able to hold any longer and the dealer refused to get the corrected paperwork they had asked for.
I called back on 8/28/15 and left messages for Jessica and Sandy.
Today I called back again and left another message for Jessica and finally received a return call. She transferred me to Sandy and she told me she was going to send the paperwork out today. I told her everything I have been dealing with and explained no tag and that I also checked on my trade and they have sent a partial payoff but still owes approx 750.00 on the trade. She told me that Jeff messed up the paperwork and he was no longer there and she did not know what had happened and apologized.
As of today I still have not gotten the paperwork. I still do not have a tag. I'm riding on an expired paper tag.
I want to know what I'm legally required to do going forward. They have really screwed up and I don't think any of this is our fault. I'm having to deal with all of there mistakes. Do I have to sign another contract?
The original guy that did the pw is not even there anymore not sure if he was fired or quit but after speaking to them again today it sounded like he screwed up alot. This is a big hassle for us.
They have paid approx 16,500.00 to payoff the trade in but when he supposedly called to get the payoff he did not get the correct amount it was acutally approx 17,400.00. They are not billing me at this point they and basically showing it paid until the 16,500 runs out. I was upside down on the car so I had 2500.00 negative equity. If I decide not to sign the new deal what happens to the amout they paid on my trade? What happens to the negative equity amount? What happens to the 750.00 still owed for the trade? Honestly if they have to keep the car and eat the negative equity I would be better off to just walk away if I get me down payment back.
I truely believe if I had not called back to check on the tag issue last week they would have never figured out that the loan had not been processed. Can I hold them responsible for anything? If so what?

You can't hold them responsible for anything, other than towing the car back to the dealer, and getting the deal straightened out. It can't be transferred and can't be registered until the title and loan has been secured. You will probably need to visit the dealer in person to get the papers straight. You do have an obligation to buy a car from them, since they have probably already sold your trade-in and they have paid off your loan, and owe them money in the deal. I would not mess around and try to do things via mail, or overnight express.

The fact that you live so far away is not really their problem, but it is yours, due to your original decision. You will need to go to them, and get the situation resolved.

Well, the dealer hasn't been paid yet so it would seem to me they are more motivated than you.

Contact the General Manager, give him the short version of what happened.