I see this as a continued disfunctional relationship. She doesnt want the focus? Well she works at McDonalds (correct me if Im wrong) and you have two kids. She doesnt have much of a choice.
You say the payment is only $12 more, but for how much longer? You say the PT is nearly paid off. So youll take a sale hit on the PT, and then keep paying $12 more for how long?
Why not disclose the actual terms and total deal for the Accord if you want honest opinions?
If your situation was different, Id think it would be a smart move, even if debt was involved. I dont think youll get much higher MPGs, or that anything will be much better just because you buy a magic Honda. And the delta in acquisition cost (youre putting another $11k out of pocket, plus interest, on a higher mileage car) would pay for a LOT of repairs on the PT.
Youre in a relationship together and for your kids. You need to make the best composite decision, not just spend money on a whim because she doesnt like something. Especially since, no offense, but I dont trust that the relationship will last. I hope and pray that it will, but if you and she have tempers and youre not on the same page with stuff, even like this, then there may be a difficult road. And if you end up getting divorced, Id hate for you to be on the hook for part of the payment on two cars, even if its "only $12 more".