RV travel brings you a kitchen, the ability to stop where and when you want, and space to stretch out. With 4 of you total, you won't need uncodable in a car, so a van / suv will be spacious. In 35 days and so much to do, would you travel quickly between spots or stay at them and enjoy- the 2nd would be a reason to take an RV. For the first I would use hotels, etc. With a rental car.
If cost is there primary consideration, then RV is not cheaper. If experience/ lifestyle is primary, then there is no match. We met a French family who did this type of Tavel 2 years ago, DM and I can connect you.