Well, if you don't understand German, reading sign on the road will be a problem, but so will be reading signs in the station.
But, as for transportation, driving might be good in So. Germany, but public transportation is great. I always start out my planning by assuming I will use the trains. Only if I find I can't get to where I want to go do I consider a car. I have only once had to consider a car, but for that, a one day car rental wasn't worth what I wanted to see.
Dachau is within the city limits of Munich and by no means requires a car.
Round trip from Munich to Neuschwanstein and Salzburg are easy connections with public transportation, and the cost of a Bayern-Ticket for all four of you is about the cost of gas, not to mention the cost of renting the car. Munich to Rothenburg with a Bayern-Ticket is also about the cost of gas.
Getting from Rothenburg to St. Goar might take a bit longer by train than by car, but the train is so much more pleasant. There might be lower fares my train but you didn't say the age of those in your party.