I would caution you on the initial part of your plan. If you are flying into Frankfurt from North America, please rethink immediately driving to Rothenburg. Even if you don't feel it, the effects of jetlag will significantly impact your reaction time, and you will need to drive on A3, one of the busiest routes on the Autobahn network. Several years ago, there was an item on a local news program about the disproportionate number of accidents caused by jetlagged travelers on this route, since it's the main artery to Bavaria, the most popular destination for most North American visitors. If you absolutely must rent a car right away, consider staying the first night in either nearby Büdingen or Seligenstadt. Both offer much of the same kind of attractive old buildings as Rothenburg, and Büdingen also retains it's defensive wall. For all the attention it gets, Rothenburg really isn't as unique as advertised, except for all the trinket shops.
Although it's a fairly large city, Nürnberg might be a good place to stop, especially with kids. If you need a day to let the kids run feral, Playmobile Park is nearby, or if you want to experience one of Germany's better indoor waterparks/spas (there are many of these!), you could take them to Krystal Palm Beach in the suburb of Stein. Nürnberg's probably too far to drive in one day from Vienna, so perhaps Passau, Landshut or Burghausen could offer a convenient and pleasent night stay.