1.) It's not a sound idea to drive anywhere right after an international red-eye flight that passes through several time zones - if that's what you're doing. Your destinations are well served by train. Costs will be lower by train as well.

2.) Heidelberg is a major detour that doesn't make sense to me because of the many miles you are adding. The "castle" is an affair that's been done and redone over the years, OK to visit but not worth the detour. I suggest this instead:

Day 1, FRA - Würzburg for one night: W'burg is a city on the Romantic Road that you pass through anyway on the way to Rothenburg, and it has both a castle and a fine UNESCO World Heritage palace:
Marienberg
Residenz

Take the regional trains from FRA's Regionalbahnhof station - it's right in the airport. You'll have one change in Frankfurt's main station. Takes 2.3 hours total. Fare will be €44 for two as long as you know the right tickets to buy. You don't have to worry about missing a connection because you are not on a schedule - you can buy your tickets for the regional trains after you arrive at FRA, clear customs, and get to the station, from a ticket machine. The next day, it's only about 1 hour to Rothenburg. (If you chose Heidelberg instead you'd get there in just under 2 hours but then you'd have an extra long trip the next day.)

Day 2, Würzburg to Rothenburg: See more of W'burg this morning. Use the regional trains to reach R'burg in the pm. €28 total for two (Bavaria Ticket day pass.) Buy it there from a ticket machine.

Day 4, Rothenburg to Munich: Then use the Bayern ticket again (€28) on the regional trains.

That's €100 in transport costs for two.

Munich to FRA: Only if you have to fly back from FRA. Purchase an advance a saver fare ticket from the DB website. This ticket will put you on a schedule but it will be cheap - maybe only €29 if you purchase well in advance.

You are a dear! Thank you. Cancelled reservations already for Heidelberg and made reservations for Wurzburg! You are absolutely right! I feel much better.

Thank you again!

Teresa

"Fare will be €44 for two as long as you know the right tickets to buy."

The right tickets are a local metro district (RMV) ticket from the airport to Kahl am Main, the first stop in Bavaria, for 8,10 per person, and a Bayern-Ticket, 28€ for two. Buy the Bayern-Ticket from an "English speaking" Bahn automat in the Regionalbhf. Buy the RMV tickets from the same automat; you can also buy them at a manned ticket counter for the same price. It will cost you 2€ more if you buy the Bayern-Ticket at the counter. Take any S-Bahn to the Frankfurt Hauptbahnhof. They run every 15 minutes. You'll get off the S-Bahn in the underground station. Come up to the ground level part of the Hauptbahnhof and find an RE to Würzburg. They leave hourly, at about half past the hour, from track 9 or a track nearby. The RMV ticket covers the S-Bahn and the RE up to Kahl. At Kahl you don't change trains, just tickets. The Bayern-Ticket covers you from Kahl to Würzburg.

The next day, if all you are doing is going from Würzburg to Rothenburg, two single trip tickets, at 13,30€/person will actually cost slightly less than a Bayern-Ticket. However, if you purchase a Bayern-Ticket, it will also be valid for streetcars and buses in Würzburg (Verkehrsunternehmens-Verbund Mainfranken) earlier in the day. Marienberg is across the river on top of the hill. There are streetcars and buses to get there; the Residenz is in town.

If you use the Bayern-Ticket for Rothenburg to Munich, it will also be valid for all conveyance in Munich (S-/U-Bahn, trams, buses) when you get there.

Germany, particularly Bavaria, has the best rail system in Europe. Everywhere you are going has rail stations. There is no reason to rent a car.

BTW, I've been to both Marienberg and the Residenz. I much prefer Marienberg. Fortresses interest me; I'm completely turned off by over-the-top gawdy homes for people who took a vow of poverty.

Don't mean to add anything confusing, but in W'burg I would visit the Prince Bishop's Residence. If you do, be sure to see the Hofkirche on one end of the Residenze. Easy to miss if you are not looking for it. In my opinion, the Marienberg Fortress is ok but if time is tight skip it. The view of it from the town is much more impressive that the view of the town from the fortress. Just one person's opinion.

OK, Looks like Lee has covered your tix. Come back if you have questions.

Russ has steered you well! Love Wurzburg! If you are there the weekend of the City festival, it's a great atmosphere. Also suggest looking into having dinner at one of the hospices. Lonely Planet and RS will have more details.

We just returned from Germany and did exactly what Russ suggested. All transportation was easily done by train. Started with Frankfurt airport to Würzburg. Went to a local weinfest in Würzburg which was so much fun! Be sure to walk out on the Old Main bridge at night where people gather to drink white wine from the little wine stand and listen to street musicians. Beautiful views and great atmosphere! Rothenburg was like being in a storybook. The town is adorable, but we really loved Rick's "walk in the countryside." Munich was amazing. We had a really nice time walking through the English gardens to the Chinese Tower Beer Garden. Also, a big surprise for us was Munich's museum quarter. There was a heat wave while we were there, so we went to all 4 museums and were very impressed! Happy travels!