Thank you for the additional information. I am sorry to hear of your dilemma. I realize how frustrating this is for you and I hope to provide you information which is accurate and useful, even though it may not be the news you were hoping to get.
Unfortunately, there is no general right to cancel a contract for a car after you sign. While there is no deposit yet, if you have signed over the trade in, it may be hard to get that back.
In any event, you would have exposure for liability in a reach of contract action, but most car dealers are in the business of selling cars, not suing potential customers. They will just sell the car to the next customer.
That being said, there is nothing preventing cancellation by agreement. So, talk to the dealer and tell them you want to back out and get your trade in back. Hopefully, you will be able to prevail on them, even though they have no legal obligation to do cancel the contract.
I am sorry. I wish I could tell you otherwise, but I want you to be prepared for the push back when you go in.
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