"My questions are: car or trains...which is more affordable?"
The answer is usually the train. But there are other important and often overlooked considerations as well.
With just 7 nights and the large amount of territory they are covering, Donna and her DH have some time considerations.
How long does it take to pick up, inspect, and later drop off the car?
Do they want to spend time planning their road routes, navigating, looking for parking, reading parking regulations in German, and paying parking fees?
Do they mind spending time waiting in traffic, getting lost, and pulling off for refreshments and a pee, or to take a rest?
And do they want to spend time doing driving/car tasks, or just sitting on the train and enjoying each other's company, perhaps with a bottle of Franconian wine?
There are certain unpredictable financial and safety considerations as well. These and other boards are full of stories of unscrupulous rental agencies who try to ding drivers for dings that weren't theirs. Radar guns all over the country will catch you if your foot is a little heavy and send you a pricey souvenir.
If jet-lagged, do Donna and DH want to be driving drowsy in unfamiliar territory? A nap on the train might be a much better choice.
Even if you're wide awake, it's important to remember that over half a million people are injured in car crashes every year in Germany.
I've actually driven a good bit in Germany on separate occasions, but each time, I wished I had used the trains.
If I were disabled or couldn't manage my own luggage easily, I might consider a car in Germany. But for a short trip like Donna's with specific destinations that are well served by an efficient and less expensive public transport system, it's hard to see any advantage at all for the car.
Visitors who choose to drive at current rental rates and with gas at around $7/gal. can reasonably be called auto enthusiasts.