This would be a BLAST to do. It takes some research and work on your part, but can be done.
There are other options besides shipping your own vehicle, such as Renting. It's much less stress & work, but expensive. Another would be to have a company in say, Germany or Belgium, "buy" an RV for you for licensing, vehicle tagging, suppling a European address, insurance, etc. The kicker is even though you have paid the funds for purchase, it belongs to the European agency. Perhaps some legal reasons that you can't bring said RV back to the states, and have to store in that country. You would need to research this.
As this isn't an RV forum, I will furnish a few interesting links from 3-4 families that have done exactly what you wish to do. The age demographic is all over the place, so something for everyone.
1st-- Rick and Kathy Howe from http://www.travelin-tortuga.com/Travelin-Tortuga/index.html. They have traveled all around everywhere in their own RV for the last 15 years +-, covering Europe and beyond for the last 5 or so years. They were recently on their way to Australia. A wealth of travel information for Schengen issues as it relates to non-Schengen dwellers, shipping their vehicle. Age demographic: Retirees
2nd-- Mali Mish from https://malimish.com/. Family of 5 now in a Sprinter 4x4 DIY camper exploring across Europe. They also have a YouTube channel. Age demographic: Working Digitally with Children
3rd-- Wheeling It from https://wheelingit.us/2018/01/21/moving-to-europe-i-overcoming-fear-inertia/. This couple RVd the North American Continent for Years and have now relocated to France. Wealth of information on immigration, visas, traveling Europe in an RV, etc. Age demographic: Working Digitally with No Children
4th-- World Towning from World Towning on YouTube. Family of 5. Homeschooling their children around the world. Relocated temporarily to France. Bought an RV traveled around Europe and have now relocated to a Catamaran to sail the seas. Age demographic: Working Digitally with Children
5th-- I will add myself, once I win the lottery. :)
As most of most of us are not traveling due to COVID-19, hope these sites are helpful, or at the very least provide some fun reading/viewing.
Sorry I couldn't get the addresses to hotlink.