Here's how I'd suggest you start. Forget for a moment about the free lodging - ignore the fact that you have a free place to stay there (and even ignore that you have family there). You need to focus on where you want to go and what you want to see/do. Figuring out how that aligns with free lodging and family visits should come after you first figure out what you want from your trip.
Start with a clean sheet of paper. Make a list of all the places that everyone wants to go to most. You can ask everyone for their input, put down as many places as you want (at first). OK, you have your starting list (perhaps a long list). Next, you need to whittle that down to something manageable. Pick the 10-12 most important places from your list. Give everyone a vote or two (maybe as adults - and as the ones who are paying for all this - give yourself an extra vote or two). Now you have your "short list" of maybe a dozen places. Next, you need to prioritize this list: re-order the places on your short list by priority, top to bottom. Now you have your prioritized list. Next, divide your prioritized short list into 3 buckets: top third, middle third and bottom third. Now you have a prioritized list of places you want to visit, and a rough categorization (must see, really want to see, and nice to see if you can). Next, print out a map of Europe (so you can write on it). Get 3 different color crayons or markers (say red=top, green=middle, black=bottom). Draw a big, fat, bold dot in red on the location of your top category destinations, a medium-sized green dot on your middle category destinations, and a small black dot on your lower category destinations.
Now look at your map. Start with the big, fat red dots - these are the places that are most important to you. Is there a logical routing you can figure out (connecting most places by train if possible)? How about if you add in the medium dots? Add the small dots, too. At this point, you can probably see some obvious geographic clusters (and challenges). This is where you need to figure out how you might string together a rough itinerary. This can take some time, but start with the assumption that large and medium cities are best connected by train. "Countryside" sometimes is better done by car, but long distances than span national borders rarely are cost-effective by car. See the posts above for some hard truths about driving.
Use your map with dots to try and rationalize your routing. If you see a dot that's waaaay off to the side (Barcelona, perhaps?) you should consider saving that dot for another trip. If there are small dots clustered near bigger dots, or right along your route, great - it probably makes sense to try and add those (be careful though, not to try to squeeze in too many stops). You have 3 weeks. You should be able to see a lot (much more, in fact, than your original plan suggests).
Then, once you have a rational rough plan based on where you actually want to go and how you might go there, then (and only then) take another look at your dots, and add dots in a contrasting color at the places where you have "free" lodging - do those places still make sense? Or would you be skipping the places you really want to see so you can save some money on hotels? How much would it cost you (in money - and lost opportunities to see the things you want most) to "save" that money? If visiting loved ones (as opposed to just sleeping in their homes to save money) is a major factor, then that should be on your list of places, just like Paris and Vienna - prioritized along with other things you want to do/see.
If your dream is to be in Paris and you don't really have much interest in Barcelona (or Cardaillac) then go to Paris and send a postcard to Auntie in Barcelona. Life is short, and you may not have too many chances to go to Europe. Make sure you use your limited chances wisely.
I hope some of the above is useful. Good luck.
