@Linkat,
After reading all this - if you really want to go on the vacation - and it seems it as much that she does not want to drive - offer that you will drive all of it or the majority of it.
Funny when my husband and I go for a long road trip - I always offer to drive but unless he is really tired he never wants me to drive (not that I drive poorly) - it is just he likes to be doing something and not just sitting there.
Another thought is - since you probably would be saving the gas money - (to me this seems a bit weird because as a couple we pretty much equally share our money) - but offer to give her $50 for the mileage -
to me the whole thing seems pretty weird as I would think as a couple you both want to lower the cost and have the comfort of the trip and overall it seems that using her car would fit it for both of you.