It is a very nice drive, but as there are no major sights along the road as between Füssen and Garmisch, it's also not a must. You will see enough mountain scenery on your way from Füssen to Berchtesgaden.
Unless you want to take a look at Lake Constance, maybe do a short boat trip on the lake, and visit old town Lindau.
You would not have to take the German Alpine Road (B310/308) back same way.
From Lindau, you can go to Bregenz/ Austria and take 200/198/179 back to Füssen.
As that loop trip from Füssen would take its time, it would only make sense IMO if you had stayed in Füssen for another night and did that loop as a day trip.

The most scenic part of the German Alpine Road (Deutsche Alpenstrasse)is between Reit im Winkl and Berchtesgaden. Frome Fuessen, that is about 4 hours driving time on the route I'll be showing you.

If you want to add a day to your trip, with an overnight in Lindau, you could go the following way, without a repeat coverage ove distances you have travelled.

Drive Fuessen - Reutte - Weissenbach am Lech on Austrian Route 198. From Weissenbach take Route 199 to the Oberjoch/Hindelang via Nesselwaengle. In Hindelang pick up the German Route B-308, which after Sonthofen becomes the Deutsche Alpenstrasse, going Immenstadt, Bad Oberstaufen, ending at the Autobahn A- 96,coming from Munich. Drive the 4km on the Autobahn south to Lindau That drive is about 2 1/2 hours from Fuessen. Stay on the island, preferably in one of the hotels at the harbor. Possibly take a round trip by boat to Bregenz, where you can take the cable car to the top of the Pfaender, which offers a great panoramic view of Lake Constance (Bodsensee) and some of the Swiss and Austrian Alps.

On the next day, on your way from the island back to the mainland, stop at one of the German service station and buy a toll "vignette" for the use of the Austrian Autobahns. Be sure you have that vignette BEFORE you get on the Austrian autobahn; if you get caught without it, it will cost you EUR 140 on the spot. The Vignette costs EUR8 for 10 days for use on all Austrian autobahns.

Take the Autobahn A-14 to the Arlberg tunnel and on to Innsbruck (after the Arlberg, the Autobahn becomes the A-12, don't ask me why). Drive past Innsbruck to Exit 59, Oberaudorf. (FYI: In Europe, autoban exits are not numbered by the distance from the state line -as in the US, but sequewntially.

At Oberaudorf head east on the Austrian Route 172 to Walchsee, Koesen, Reit im Winkl (in Germany). In Reit, follow the signs to the B-305, Deutsche Alpenstrasse. It takes you to all the way to Berchtesgaden, and is again a section of the Alpenstrasse. From Lindau, the trip takes about 6 hours driving time. THe whole trip from Lindau to Oberaudorf, and then to Berchteshgaden is all very scenic.

If you want to skip Lindau, from Fuessen take the Austrian Route 179 to Lermoos and then the Routes 187 (Austria)/ B-23 (Germany) to Garmisch-Partenkirchen, and in Garmisch pick up the B-2 to Mittenwald, and the Austrian Route 177 to Zirl. Between Mittenwald and Zirl, get your Vignette at any German or Austrian service station. In Zirl pick up the A-12 toward Innsbruck, and continue as above to Oberaudorf. The Lermoos to Zirl is also a very scenic drive.

Actually we are planning a two night stay in Fuessen, so perhaps that might be a plan, thanks. Our other option, since from Fuessen we are planning to go up the Romantic Road, we were thinging a cross country drive from Lindau up to Augsburg perhaps???

thank you so much Treplow for all your help!! We were going to have a night in Innsbruch as well, so that may fit in nicely. Will print your route out and take with us