Dealership demanding car back.

Arizona.

The story:

Went to dealership with a trade-in. Everything was fine, drove away with the vehicle. Two weeks later they want me to sign another contract. I oblige. (Side note: This contract was stamped with the same date as the old one.) About 4 weeks after signing that 2nd contract they call me and tell me financing fell through and that they need the car back. I did a bit of looking into it and I read that they have to notify me within 10 days or the sale is final. Is this true?

If I do end up having to give up the vehicle; They gave me $8500 for the trade-in value of my old car, my remaining loan is only about $7000. Do they owe me restitution of $1500? Do I owe them money for miles put on the vehicle? In the meantime can they lawfully tow the vehicle? What kind of lawyer should I get to represent me if I went down that road?

What other potential posturing do I have?

Thanks so very much in advance.
-Brandon

You need to read through the contract that you have. It may explain the rescission of this sale. Ariz.'s AG has a web-page where he urges his citizens to not buy cars without having secure financing.
It's not clear why you expect any restitution. If they still have your old car you can be made whole by getting your old car and perhaps some money for the financing and vehicle registrations. If they don't have your old car then you have agreed to a value of $8500 for it.
I wouldn't offer to pay anything for mileage.