Please note that this is not legal advice and does not constitute an attorney-client relationship.
You may want to retain an attorney for this matter. For one thing, once you signed a contract and gave a deposit, they cannot unilaterally change the terms on you and require that you need to pay more money. I am very confused as to what makes them able to deny your loan (which I assume that you were previously approved for or they would never have let you leave the dealership with their vehicle otherwise) after you left because you are not the primary driver. The additional $2000 that the dealership requested also seems to be a attempt to make a unilateral modification of the contract.
You should contact an attorney in your area who is familiar with the consumer fraud act and breaches of contract. I cannot say this with as much emphasis! Make an appointment to see this attorney and be sure to bring copies of both your contracts (the first and the second contract), the names of the people who contacted you, copies of your checks or the check numbers and amounts, and any other pertinent documentation.
As with the learned gentleman above, this is not legal advice and you'd have to call me before I could represent you. (Since I am admitted in NJ, I can represent you if you wish.)
As gentleman above astutely pointed out, you would never have left the dealership if you did not have some kind of approval for a loan. This is what I think happened (I have seen this many times): you got approved for the loan with $2500 down after somebody spoke too soon and told you $400 down. They want the sale so they send you home with the car hoping the "puppy dog" effect will increase the likelihood they can wiggle more money out of you later to meet the loan underwriter's requirement of a $2500.
Now, here is a critical point, do they just want additional money down (not fraud -- but still should not have happened) or are they raising the price of the car or playing games with the value of your trade-in (highly likely if your trade was "upside down" -- more money owed than it's worth). If they are actually raising the price (the total you'd pay for the car in the end), you have a per se (i.e. slam dunk) consumer fraud case under NJ's very stringent consumer fraud laws.
To be fair to the dealership, however, it is quite possible that, in this economy, the bank is changing the deal and wants more down in which case you and the dealership are both victims of the bank's unethical practices. I'd have to see the papers to have half a chance of figuring out who the "bad guy" is in this scenario.
If the loan was contingent on certain conditions that did not happen, you really must "undo" the deal. If you tell them that's what you want to do, you will have considerable bargaining power as they can no longer sell that car as "new" given that it has been titled and (probably) driven over 1000 miles -- making it a "demo." This would turn the tables on them who are likely betting that your male ego will get in the way of returning a car that was a gift to your wife. (Take your wife with you and have HER tell them she is sick of the whole mess and wants her old car back -- even if you are both bluffing.) Good luck -- and please get some advice from an attorney.