Can a contract be altered after sale is finalized.

I bought a vehicle and sign a contract. I trade in a Vehicle and put a down
payment. I still owed on the vehicle I traded in. They told me it was no
problem and that it would be rolled into the price of the new vehicle.
Everything is on the contract. But, now the dealer is saying that I need to
pay $2,000 more because the bank will not finance the amount that is stated
in the contract. They are telling me to either pay the price or take back
my old vehicle. And I want to know if that is possible for the dealer to do.
If we signed a contract. I need help!

This unfortunately is a common event and one that is unacceptable. Depending on what you signed you may fight it--and sue in small claims (even if the contract says otherwise)--you could argue they said it was a completed deal and you relied on it. Otherwise they must give you every dollar back and let you go to another dealer--