Nuremberg and daytrip...which pass or car ?

The knock against Rothenburg isn't that it isn't worth seeing or that it's too touristy (although it is, kind of). It's that it isn't unique enough to justify going far out of your way to visit. But it's convenient enough from Nuremberg, so why not check it out?

Parking is not particularly difficult in any of the cities or towns you mentioned. Most of the stuff that people visit in Nuremberg is easily accessible from the Hauptbahnhof, and there's always parking available there. You can't take a car into the walled portion of Rothenburg, but there's usually plenty of parking outside.

we arrive from Dresden via Erfurt (we will stay 4 hours in Erfurt) . The train ticket is already buy. We need to go from HBF station to Ludwig strasse (near Plärrer Ubahn station). Can we us the Ubahn with our train ticket ? We wont need to move again on that day. <<

It depends of the type of ticket you have. If you have a »Quer durchs land Ticket« or a long distance ticket with the additional remark »+City«, you can, else you cannot, sorry. If you want to save money, it's a 10 minutes walk from Hbf to Ludwigstrasse (easy to find).

Day 2 (july 20): Playmobil park in Zindorf and walk around town (nazi rally ground maybe)
Day 3 (july 21): Daytrip to Bamberg and walk in town.
Day 4 (july 22) : day trip to Wurtzburg and Rothenburg
Day 5 (july 23): leave for Salzburg
<<

Day 2-3: get a »Tagesdicket Plus« from any DB oder VGN ticket machine, e.g. at the Plärrer Subway station. The price is 18.70 E. for the family. Day 4: Bayernticket, if you do both (subject to the 9am restriction), VGN ticket if you do just Rothenburg (not subject to that restriction).

Maybe Rothenburg and Wurzburg could be too much in the same day, which one would you choose ?

Rothenburg. Even if it is described here often as a sort of touristic plastic town, it is a well preserved medieval city and one of the most important focal points in the develeopment of European romanticism (and nobody forces you in in those awfully kitschy christmas markets, which are frequented by Americans and Japanese). Würzburg has one outstanding attraction, the Residenz (Napoleon said, standing before it »What a remarkable presbytery«), the rest (cathedral, medieval Main bridge, Marienburg castle) ist nice enough, but cannot compare to Rothenburg.

You can do both if you depart from Nürnberg right at 9:05 to W., reserve 3 hours for Würzburg and depart from Würzburg to Rothenburg 13:41. This gives you five and a half hour (or seven and an half hour, the evenings trains leaving at 20:06 and 22:06) for Rothenburg.

Maybe we could rent a car for 3 days (july 20,21 and 22) but I guess parking >will be a lot of hassle in Nuremberg and Rothenburg.

Not in Rothenburg, there are plenty of parkings along the medieval wall; in Nürnberg there are a lot of parking garages, but at a price. In my view, for your program you don't need a car. E.g., for the Nürnberg - Rothenburg trip the fastest train connection is 1:15, by car you might do it in 1:00 for a much higher price. For the Bamberg and Würzburg trips the train is faster.

Nordlingen seems nice in that aspect too but that pace is not easily accessible >by train.

It is nice, but it cannot compare to Rothenburg. Access by train is via Donauwörth (shortest travel times 1:53 to 1:57).