Don't assume that the Czech Republic is the only problem with a rental car. I've had Hertz vehicles at CDG where the standard contract is that they cannot be taken out of France.

IMO it's better to stay in small towns and rural areas or enjoy scenic drives when you have a rental car, taking advantage of the flexibility to visit such places conveniently, and conversely to visit big cities on other trips when you don't have the car. I try to avoid mixing the two on one trip or at least to do the two different types sequentially rather than mixed together.

Can you do the rental car for only part of the journey, such as the Rhein area, returning it back to the same place (FRA), and then either fly or use (fancy express) trains for other portions? I guess I don't see the point of going into Prague just to stay overnight.

If elderly people have mobility issues, most trains (which typically don't require steps to board and exit at major stations in Western Europe) would be better than getting in and out of a van. Plus, the train has lavatories on board, so there's no need to find a good place to stop for bathroom breaks when driving.