Family trip to Europe in Summer of 2022 w/2 kids

Have you considered an open jaw ticket? Flying to Frankfurt and home from e.g. Milan or Florence? Also, taking the train instead of driving south saves you having to make sure you have all the vignettes etc.

Check out Landhaus Armstorfer on booking.com near Hallein, Austria. It’s about 20 minutes south of Salzburg, 20 minutes from Berchtesgaden and an hour from Hallstatt. There’s a somerrodelbahn near Hallein that was fun. There’s a salt mine in Hallein, but we went to the one in Hallstatt. Just south in Werfen is a great fortress and an ice cave. 2 br, 2 ba with stunning views. We stayed there for 5 nights in June 2018.

Finding a good Sommerrodelbahn is always fun. If your girls like the Sound of Music (and even if they don't), Salzburg and the surrounding area is great--the Wolfgangsee, for example, is amazing and surrounded by great hiking. There is a lot of "easy" hiking depending on your and your grandkids' activity level. The salt mines are a fantastic experience that I did with my grandparents back in the day.

If you want to inspire them from a social standpoint, consider the history of the White Rose movement for Munich, though in terms of sites there are not many--but it's a good conversation piece. Dachau is also well worth a visit in that region, but of course it depends on the maturity of your younger granddaughter. For a chance for the same conversation but without the horrors of a KZ, the Eagle's Nest offers the contrast--the oppressors vs. the oppressed at their most extreme.

For lodging, I would search for a good Gasthaus in places like Berchtesgaden or Garmisch; I don't have specific ones, but these are a great way to get a more authentic and intimate lodging experience than a hotel.

One last tip: Book the Neuschwanstein tour time at least 24 hours in advance, preferably more if you want a good time. Take the carriage or walk up, then hike down the back way through the gorge along the water.

Take the time in Italy to visit a Medici villa and talk about the concept of oligarchy.

Your granddaughters are lucky to have you! They will remember this trip forever!

Both the Neuschwanstein and Hohenschwangau Castles are located within walking distance above the little village of Hohenschwangau. It's a cute place! What we did was spend the night there and then visit both castles the next day before driving on to Munich via the Wieskirche. The castles are very different so visit both!

" I've already received some good lodging tips for Italy but would appreciate some for southern Germany (Bavaria) as well."

So far you've gotten the name of an Austrian inn but nothing in Germany. Maybe the meager response is because any suggestion would be a wild guess at what your needs and wants are. What criteria do you have in mind for a good stay?
In the places you have named, a hotel room for four may not be so easy to find; apartments tend to be more numerous. I generally tend to rely on online descriptions and reviews to narrow things down - this makes it easier to find what's available for my specific dates and for my needs.

Since there are four of us, an apartment or something of that sort might work. A place with at least one separate bedroom and another room with at least a sleeper sofa would be the minimum, and frankly our girls are getting too big to expect them to share a little sofa bed. I suspect we may also be open to two separate rooms in a gasthaus. As a military retiree I'm eligible to use the Edelweiss Lodge in Garmisch but it may not have rooms available when I need them so that's why I'm looking for other options.

a few days in Germany (Bavaria after flying into Frankfurt)

It's good that you are looking around now because between all the Passion Play Pilgrims in Oberammergau and the expected throng of visitors in what will be a break-out year for pent-up tourists, you will see a lot of competition for rooms/apartments.

Except for Berchtesgaden, in Bavaria's southeast corner, all your stated travel goals lie within fairly small travel radius. If a few days means 3-5, and if "etc." also means places like the Zugspitze, the Wieskirche, Ettal Monastery, Schloß Hohenschwangau, Schloß Linderhof, and Mittenwald, then you have a LOT on your platter - maybe too much for a few days - in that same smallish area. So I will respectfully suggest you might forego Berchtesgaden and instead spend all your nights (minus your first night) in a single location in/near Garmisch. Finding and staying in a single place should be a lot more doable for this short time, especially if it's an apartment rental (or "holiday apartment," which often requires a minimum stay of 3-5 nights.)

The Garmisch tourist office booking site is a very comprehensive source. Search in the farm house / holiday apartment / holiday home categories and filter by bedroom options. 83% of the 400+ listings are holiday apartments. If you find something that is both suitable/attractive and available, you can usually turn up user reviews by googling the facility or its address.

In a separate thread I think I cautioned against taking on too much on your day of arrival at FRA. It is a very long drive to the Alps from there, one that I would not plan on making that same day (the effects of jet-lag or drowsiness after a red-eye flight across several time zones can be unpredictable and unmanageable.) It would be wise to spend the first day/night somewhere near Frankfurt; perhaps you could make a little southbound progress toward the Alps by driving (or catching a train) up the Main River to a local Gasthaus in a nice town like Miltenberg.

For Russ:
Thanks for the excellent tip on the Garmisch Tourist Office web site--we should be able to find something there. Don't worry about our long drive from Frankfurt--we've decided to head the other direction first and go to Paris, then on to the UK, then we'll circle back to Germany again and then northern Italy before departing from Frankfurt. We're probably looking at 3-4 weeks. So we'll probably end up spending the first night in the Frankfurt area before catching the train to Paris, so the next task will be to find a good place to spend the night not too far from the airport/trains.

Heppenheim is an attractive wine town with half-timbered buildings and lies south of FRA airport - might be a doable and enjoyable stop for your first day/night:

https://www.heppenheim.de/en/heppenheim-erleben/tourism/
https://www.heppenheim.de/en/heppenheim-erleben/tourism/uebernachten/

Hi DK- Why don't you fly open jaw into the UK, then go to Paris, then Frankfurt by train. Then pick up the rental car in FRA and do Germany and Italy. Then back to Frankfurt (or Munich) to turn in the car and return to the US? That would save the time and cost of half of the Frankfurt - Paris- UK - Frankfurt circle.
Another thought- I believe driving in Italy with a rental car is not as simple (or inexpensive ) as it was a few years ago. Be sure the rental car company is aware of your intention to drive to Italy when you make your reservation and again at the rental car desk in Frankfurt. FYI, the rental car selection at the FRA airport is (usually) much better than at other places around Frankfurt.
Have a great trip!!!

One idea not yet floated is to stay in a hostel. Many hostels are more like hotels. You can get a private room, and often they are inexpensive. The bonus is that there are many school groups staying there. Your grandchildren might meet some German/Austrian kids. We've never been unhappy doing this (we are 69 and 72 also). For instance, in Munich, we stayed in Hostel 4you. Good breakfast, very close to the Hauptbahnhof, close to the old town area (walk or streetcar). I just checked - you can get a 4-person room for $120.

https://www.hostelworld.com/hosteldetails.php/The-4You-Hostel-Munich

I would also get the 14 YO involved in the planning. Give the child a city to look up, and find the fun stuff to do.