I agree. You tried - twice ! We all have the luxury of hindsight on this. But I'm not sure we would have done anything different if any of us had been sitting there in real time.
And I find nothing wrong with your original statements. It sounded to me like your wife had done some PRELIMINARY bargaining and the dealership threw out a number.
If I was sitting there when you came back, my view would have been - When they knew you were ready to buy, they came up with the 'best and final' price. You then said - 'Are you sure ? '. Twice.
Who among us has ever bought a car, truck, boat, or RV based on the dealer's beginning offer ? I sure haven't.
Tim