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It appears that the financing has already been contracted and approved as we agreed upon a week ago. That is where I'm confused, whether or not this contract indicates what I believe.
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We have some guys here who are experienced in the auto industry, so they should correct me if I'm wrong.
My understanding is that your average car dealer - esp. used cars (because they're smaller, not any issues of shadiness) - often use 3rd party lenders to finance their buyers' purchases. So, if I buy a GMC from a GM dealer, my loan might not be through GM directly, but perhaps through a national credit union. If I buy a used car from a small lot, it might be through a local bank.
With that in mind: some dealers have enough volume where they can send the information and get instantaneous approval from the bank. As in - you have a loan the same day.
But, if it's a smaller dealer, I might give the dealer my info, and the dealer will agree to find financing for me at X% on Y terms - it may not be instantaneous, and could take some time for the dealer to find a lender. Even if you've made a down-payment and have actual possession of the car.
Being as that lag exists, it may turn out that no bank is willing to approve the loan (lots of factors: many small lenders won't finance a car 5+ yrs old regardless of your credit, for instance). If that's the case, you're looking at a contract that may be impossible to perform - despite the good faith and best efforts of both parties.
Is that latter what's happened in your situation? Maybe not, and you'd certainly be within your rights to cancel the contract, but then you're out the car on terms that were apparently agreeable to you. But, I'm guessing that something along the lines of the above paragraph is what happened.
My recommendation on reconsideration: if financing is available for just you, and it's at a lower rate, just do it. Leave the AG out of it. Nobody benefits from that.
There are a lot of ways, that are probably better, to improve her credit. For instance, get a very small credit card (as in $1,000 or less), and have her buy one tank of gas a month, and pay it off on time every month. Just as good as having a car payment, and maybe even better because she might gets points on the card.
In fact, you could probably get the dealership to help you out with that. Say, "as we're changing the terms of the contract because
you couldn't do what you said you'd do, why don't you arrange a credit card through the same lender for my fiancee with a max. limit of $500. You make a sale, we have a car and no reason to badmouth you."