Dealership Threatening To Report My New Car Stolen

Location: TX

I’m dealing with a terrifying situation right now with a dealership and need some advice.

Timeline: I needed a car cause my old one broke down a while ago. My dad offered to help chip in by offering a trade in car and putting a down payment for me to finance a new car. We went to the dealership and we decided on a car, my dad wrote the check but he was wondering what the total price would be for the trade-in car. At first, they did not want to give a price on it without seeing it in person but after some persistence from my dad, they decided to give a blind value to it. My dad had then left and I signed all the paperwork such as the installment contract. They told me that I could bring in the trade-in vehicle whenever.

I brought in the trade-in vehicle a day later, they state that the vehicle is not worth the amount that they had put down in the contract that I had signed and that now they need me to either, 1. re-sign a new contract with a new finance installment to “correctly match” the value of the trade-in, or 2. they take the keys of the car that I bought and drove after that initial day of purchasing and will refund the check that my dad gave.

There was nothing in the contract that both me and the dealership signed that stated anything about reevaluating the finance installment if they change the trade-in value. In fact, there was nothing stated that they could even take my new car back if the trade-in value that they gave was actually wrong.

Now they are threatening me and saying that if we do not come to a conclusion, they will report the vehicle as stolen. They also said that the contracts that I signed are voided because they never “cashed in” the check or submitted the signed contracts.

My question is can they actually report my car as stolen when I have a signed sales contract in my hand? Is "the deal isn't funded yet" a real legal loophole they can use to cancel a finalized contract over their own appraisal mistake?