Car vs. Train from Frankfurt to Rothenberg to Gunzburg?

If you go to your hotel first, you won't be toting them around with you, nicht wahr? Even if your room isn't ready, you can always leave them in the luggage room or behind the front desk until your room is ready.

There should be some parking garages near the Roemerberg. Rothenburg has parking lots outside the city walls.

How many is "we"?

From Frankfurt to Rothenburg ob der Tauber requires two train connections, from there to Gunzberg is 3 connections, and then back to Frankfurt can be done on a direct train a few times per day. Packing light would really be the key to navigating these train connections.

I'd be more likely to pick up a car when departing Frankfurt, not at the airport when you're jet-lagged and could just head into the city by local train. All the major agents are represented at the main train station and "Train Station" is a typical location description when reserving a car online. Parking in Rothenburg is easy in parking lots outside the walls. To park at or closer to your hotel, ask them at the time of booking.

And then could we return our car in Gunzburg?

You can but possibilities are limited to Hertz (at the station) and EuropCar (200m away). A larger selection of car rentals is in nearby Ulm. If you decide on the train (maby you don't want to drive in nasty weather and darkness), book your tickets for the Günzburg - Frankfurt leg asap since prices are already going up for that connection.

From Frankfurt to Rothenburg, it’s only about 85 miles and the roads are good. My wife and I prefer to drive since it affords a freedom that train travel can’t give, i.e., being able to stop when and where you want, and not being dependent on a train schedule. That being said, it’s dark by about 4pm and you could end up driving on unfamiliar roads, or in towns at night trying to find a place to stay or park. Weather can also be a factor. Years ago in a December when my son was stationed in Holland, it was nice and clear when we left his apartment in the morning and we were in a blizzard driving back to it later in the day. Also, while there is parking outside the walls of Rotherburg, if its Christmas is popular, parking could be an issue.

We used a company called "Day Trip" for transportation between stays and were well pleased with them. I've never used Uber but I think "Day Trip" is very similar to Uber. Check out their web site.....they aren't a ton more expensive than renting and they know the territory.

Consider taking buses. We took the bus from Frankfurt to Heidelberg. The time was about the same as the train, the cost almost the same, the bus comfortable. If you have several train changes, there may be a direct bus. And in most stations, you can leave your bags in a locker.