Let me ask this -- IF you'd sent a check for $9000 too much, do you think the dealer would have sent a refund?
And, a very old game in auto sales, sell a car, let the buyer take it home, call a couple days later and say they made a mistake - a mistake never in your favor.
What does your contract say - if it has the price you paid, then you own it. Just a personal opinion, I believe you got the right deal, and the dealer heard your wife, and is now trying to raise the price. That's just my opinion, but it's my opinion because I've seen it happen.