YellowJacket:
As a former carsalesperson (and one who is suspicious of all salespeople), I wanted to be on your side...but I'm not.
This is more my speed.NADA.com does not take into consideration condition of the vehicle. All vehicles there are assumed to be in excellent condition, and you started this chat by saying that your Impala was anything but. KBB.com, on the other hand, does have four levels of condition. I ran it based on "good" (not the top rating but above what I THINK your car should be, based on your description) and found it to be similar to the number the dealer gave you.
And you want around $10,500 for a trade? That's nearly 100% more than it's worth. You're "upside down," and a dealer's nightmare. The only way I could see you getting your car paid off is by either tacking the current loan onto the new car (which is what you've described) or finding a more expensive car where they can sell it to you at MSRP and hide the $4,000 loss in the "profit." Neither one is going to make you happy.
It's not always the dealer's fault. You owe too much on the car, you expect too much for the trade, and you expect to get a base model in the deal. I understand the desire...but you have to understand the reality. Nothing's free.
The math is simple: you want a $15,500 car with a trade valued at under $7,000 with somewhere around $10,500 owed. That's approximately $19,500 plus tax and tags.
Sell the Impala for $10,000, taking a $500 loss. Buy the car you desire (Altima or G6 or whatever) straight with no trade. That's my cent and a half (inflation, you know?).