Ok, so here's one way to convince her. You both must ignore everything that has happened in the past.
Today, you have a car worth $19,000, A loan of $27,000 at 8% (60 months? 72 months?), $26,000 of cash(I'm assuming guaranteed from something), and a need for a reliable vehicle of some sort.
A reliable, relatively fancy, and excessively large vehicle can be had on the used market for between $10,000 and $15,000.
If you keep the current car and pay on your current loan and use the cash for something else, you will pay (60 months at 8%) about $33,000 for the Navigator.
Lets say you use all the money and pay off the loan and keep the car. You now have a car, no loan, and no cash (actually, -1,000 from the additional you had to pay above the cash you had), but at least you didn't lose an additional 6K in interest.
If you sell the car for $19,000, and pay of the remaining $8,000 today, you cut the extra $6,000 of interest lossess over the next 6 years. You now have $18,000 in cash and no car. You can now buy an acceptable $15,000 car (with cash, no interest). You now have $3,000 to pay down other debt, and a reliable car, and no loan.
Which option is better? For heavens sake, even if you use the $3,000 for custom made leather boots, diamond jewelry, and a vacation you're better off! Perhaps to help persuade her you could identify some $15,000 cars.