Hi and welcome!
We have made several trips through the Western US and Canada in rented RVs. In fact, our first RV trip ever was in a rented Class C from Cruise America. It got us hooked.
Thousands of people from Europe do it every year. It is not difficult.
1) I believe you need not worry about your drivers license. As far as I am informed, you are good to go with a rented RV in the US. If unsure, clarify with the rental company before booking. The international license has never interested anyone in the 15+ times I have traveled there.
2) watch this orientation video by one of the big rental companies. They show it to every renter. It is good, basic info:
https://m.youtube.com/watch?v=GKdr4Z1LBKY3) The intimidating size of a small class C is not an issue on American roads. Plenty of space. But watch your height, especially trees on parking lots! It takes some time getting used to it.
4) The West is very wide. Very much unlike Europe. Plan less, and spend more time looking, hiking. Go to smaller locations, not just National Parks. There are many, many beautiful state parks. Traffic is not an issue out West, you can plan long driving legs. But don't drive too much. You are on vacation, there is no award for most-places-visited. Restaurants and gas stations can be hours apart. Fill up as soon as the tank is half empty. Have enough food supplies with you, there may be no restaurant available where you spend the night. You are there for the beauty of the land, not necessarily for the best food.
5) I agree that the children may be too small to enjoy the trip. If you take them along, plan according to their needs.
6) I have liked spring for traveling. But the earlier you go, the colder it gets. The south rim of Grand Canyon is at over 2000m elevation! Denver is called the Mile-High city. Many areas out west are pretty high up. Some important travel routes are closed in winter and open up as late as May. On the other hand, Death Valley in February was just ... nice.
7) The best rental company is the one that offers what you want, when you want it. There are a lot of special deals for one-way rentals at certain times of the year. It may make sense to fly into one city and return from another. In Germany, we have a travel agency called canusa.de, which specializes in this sort of travel. I would think Italy has something like it. For your first trip, maybe listen to their recommendations. In any case, there is only a handful of companies catering to international tourism, Cruise America probably being the biggest. I think two smallish class C RVs would work best for you. Also, that sector has the most offerings and the best prices.
Feel free to contact me via PM if you want to talk directly.
