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So back at the end of August my bought a new Hyundai from a dealership in WA. I wasn't too fond of Hyundai cars but I supported her decision that she wanted to trade her BMW X-1 for this brand new car. So they were of course trying to get her to use their finance but she used USAA who she is finanaced with now with on the BMW . The deal gets done and my wife is watching her USAA account to see when the BMW pays off from Hyundai. Fast forward and here we are to this day and the car still has not paid off and my wife of course has to pay on the BMW and now the Hyundai note comes due in a weekI believe. Of course she's been hounding them constantly. She was blatantly lied to by a female in the finance office that Hyundai had sent the payoff to USAA which never happened. During this time I am also watching her BMW being advertised for sale and appears to have been sold or maybe they held off on advertising it. What she finally find out is Hyundai mistakenly paid a check to BMW who promptly cashed that very check knowing there was no car financed by my wife at BMW. The Hyundai dealer had even called her early on to ensure it was USAA for the payoff because they saw BMW on her purchase order. Finally talked to the General manager on Wednesday who claimed he didn't know this was going on and promised to send a check to my wife for her extra payments. They're right across town and no check yet. They claimed they fired that finance person who has done this before and reprimanded the person who told my wife that "misinformation" about a check being sent to USAA via FedEx like 3 weeks ago!
I just had a similar situation.
Bought my Lexus on July 12th. No registration sticker for new car or payoff on old car for almost a month. Got a letter from the DMV that the registration on my mazda was renewed with the new lienholder being the dealer. Forwarded everything to the sales manager, who was very apologetic and transparent and CCd me on the office communication. Joked that since it was still registered in my name, I was going to get a spare key made and go pick it up off the used car lot. There were no LOLs had by him.
Finance office claimed that they sent off the payoff weeks ago so I called Chase and they hadn't received anything and the 14 day payoff was long expired meaning the agreed on purchase price of the Mazda wouldn't cover the new interest charges. Contacted the sales manager and told them they need to cover the new outstanding balance. He says they'll take care of it. Few days later he emails me that the new payoff was sent out and it covers the additional interest. About 2 days before the payment was due, Chase updates my account to 0 and I spend the next 2 months watching the account for a residual balance to pop up, but it didn't. Chase actually closed the account within a week.
At about the 6 week mark, I get a notice from the DMV that they were suspending the registration on the Mazda and I was being held responsible. Also, still didn't have the tags for my new car. Fired an email off to my attorney with pic of all the documents and conversations attached, asking what my options were and CCd the sales manager. Sales manager responded they were personally taking care of it. About 5 days later I get my tags, directly from the dealership instead of the DMV. A couple of weeks after that, I get a refund check from the dealer for $160 in fees.
I have no idea if the Mazda is still in my name. Need to go to DMV for my truck so I guess I'll find out then.

Unreal for both of you.
If the dealership is local enough to you, you should make an appearance
and have the manager clear that all up on the spot.
And dont take no for an answer.
Good Luck to the both of you