score:6
The DB route planner does not find any connections on Saturday or Sunday because the only bus going to Mörsdorf (RMV's line 634) only operates Monday through Friday.
The closest you can get by public transport during the weekend seem to be by bus to Kastellaun, some 9km from Mörsdorf. From Kastellaun, you would either have to walk (1.5 to 2 hours) or take a taxi. There are several taxi companies in the area, so getting a taxi should not be a problem.
The Schönes-Wochenende-Ticket is however not valid on the RMV buses, but only on local and regional trains.
I also hope, that you don't plan to do this on one day? The first connection with only regional trains from Friedrichshafen via Stuttgart to Kastellaun arrives 14:44, while the last connection from Kastellaun via Stuttgart back to Friedrichshafen departs 15:35.
Upvote:2
The only way would be to take the train to Koblenz, and then take the bus from there, which takes approx. 2,5 hours. I found the bus connection only on www.vrminfo.de, so it's possible, that the Schöne-Wochenend-Ticket is not valid there, thus it's not found by bahn.de. Honestly, if you really want to do that, i'd suggest to take the train to Koblenz and then take a rental car from there.