Yes, it is too much.
One night stands are occasionally necessary, but not recommended. You are correct to be concerned about factoring in getting from place to place. Logistics can really take up time.
Night trains can help. (BTW, is your girlfriend’s agenda for the trip the same as yours?)

You need to allow half a day or so to take the train from Rome to Cinque Terre. (You might think about going first to the town of your choice in Tuscany, and heading up to the Cinque Terre from there.)
Cinque Terre Tips
From Cinque Terre, you would have a scenic train ride into either Switzerland or France.
You can, I believe, take a train from one of the Cinque Terre towns to Interlaken, Switzerland.
Depending on which train you get, some are faster than others. I think La Spezia (sp?) is the main hub.
For France, you can stay around the Cote d’Azur or maybe go further inland to Provence.
I actually preferred the far southeast coast of France (Vermilion coast) but that might be too far for you.
Circling back to Rome, you can go by way of Venice, Bologna, or the region of Tuscany (which includes Florence, but I know you said you’re not into museums). A little culture won’t kill you. Cortona is a beautiful, low key way to see both medieval and Renaissance culture in one small, picturesque town.
I’ve not been to Turin, but have actually heard good things about it.

I am sure other people can offer other points of view. One thing you might consider is inter-European flights, to save time.

WhichBudget

Once you factor in travel time you will not have much time to spend in each place. I had a similar itinerary in terms of staying in places for a night or two and after a week we were so sick of it. I would suggest 2 nights at a very minimum but 3 or 4 nights will make it much more enjoyable. If you are looking to relax I would suggest cutting your itinerary in half so you spend less time on trains and more time seeing places.