Family of 7 travel in France, Switzerland & Italy

Our family of 7 is traveling to France, Switzerland and Italy this summer and I'm trying to find the most affordable transportation. (2 Adults, 5 kids ages 18, 15, 14, 11, 9)

These are our plans:
Paris - 3 days
Paris to Strasbourg, France (1 day)
Strasbourg, France to Bern, Switzerland (next day)
Or we can travel direct from Paris to Bern if that is too expensive to stop over in Strasbourg.
Travel within Switzerland for 7 days
Interlaken, Switzerland to Milan, Italy
Then we are renting a car in Italy so we don't need transportation after that. (But will also be in Cinque Terre for 4 days).

I'd love help! Thank you!
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