We do plan on Nürnberg on a day visit from Munich. And Bamberg on our
way from Munich to Rothenburg. Definitely have time to change a few
things.
If instead you create a base-town strategy for visiting these three towns on3-4 adjacent days, you'll reduce the inherent backtracking in your current plans for hitting Nuremberg and Bamberg. Nuremberg is a good travel base town for both Rothenburg and Bamberg. Also, Munich - Bamberg - Rothenburg will involve more than 4 hours in the car, not including parking or traffic issues. But Nuremberg is varied and interesting - IMO to plan on being in N'berg for just part of one day is truly shortchanging your visit! (The same could be said about Bamberg with a Munich - Bamberg - Rothenburg travel plan.)
Want to get the most bang for Euro.
Reduced miles traveled = reduced transport costs, as a rule.
Also... don't know about total car costs once you toss in rental, gas, insurance, parking, etc. But you will likely save some Euros and some hassle if you don't drive. Nuremberg - Bamberg - Nuremberg... or Nuremberg - Rothenburg - Nuremberg... would cost €20 by train per day for two adults round trip. (That figure also includes any subway, tram, bus etc. you might use within Nuremberg or Bamberg.)
Let's say you accept this tip and stay in Nuremberg for 3-4 days... If you take two separate day trips, one to Bamberg and a second to Rothenburg, and if you do those on Saturday and Sunday, you pay only for one day. The €20 day pass is valid for one day on most days but if bought on Saturday, it's valid the whole weekend:
https://www.vgn.de/en/tickets/all-day-ticket-plus/
About getting from Munich to Nuremberg in the first place... Gas alone would cost €25 - but if you take the train instead and use the Bayern Ticket day pass, it's €31 for two adults (and this pass also includes inner-city transport.)
Hope this helps stretch your Euros some.