This is too rushed. I would advise to keep Rome and skip Naples. I've been to both and although I like Naples just fine (many don't - you might not), Rome is better for a first-time visitor, and 3 nights there is a good amount. Anecdote: a friend in her late 50s took a (guided) "trip of a lifetime" in Italy. In 10 days they went to about 5 cities. When she got back, she was dizzy and said everything just ran into each other and she doesn't remember how each city was. That's a huge pity because she wasted her money on her one trip to Europe and came out not being able to describe the feel or sights of each city. But she sure could check off the boxes saying she went to cities V, W, X, Y, and Z! Perhaps this is what your wife is trying to do too, check them off the list. Don't worry, Europe will be there even in 30 years if you want to go back and see the rest of it. Have fun!

I also hope you realize train tix in Europe aren't exactly cheap, especially if you move around as much as you plan to.