I responded on THIS thread nearly 2 weeks ago. You provided this travel window: "We leave Prague on a Sunday and fly out of Frankfurt on Friday." If that is still the case, then I'll just re-suggest trimming off Munich and that stuff to the south and focusing on the much swifter Prague - Nuremberg - Rothenburg - Rhine destinations you seem to be opting for here. The fastest and most direct way from Prague to Nuremberg is on the IC bus and takes nearly 4 hours. So on Sunday you'll have about 1/2 a day for sightseeing, then 4 days for the rest of your travel and sightseeing - just enough, perhaps, for what you have in mind.
SUN
"...would like to settle that day somewhere near Munich or Nuremberg - sightsee and then spend the night somewhere convenient and get to Rothenburg area the next day."
Let's go with "near Nuremberg." Do you want to sightsee in Nuremberg? That would be pretty simple. Arrive around noon, stow bags in a locker. Spend several hours there seeing what interests you and have a meal: Nuremberg sights
Then, just take the train to Rothenburg for 2 nights. The 17:21 train gets you there at 18:49, the 18:36 arrives 19:49 and will cost €17.50 for your family using a "Tagesticket Plus" daypass.
MON
Rothenburg
TUE
Train to your Rhine town of choice. Bingen is a smart choice for 3 nights if you want to reach FRA early when you fly out. Suggest a stopover of maybe 3 hours in Würzburg - you'll get there about 1 hour after leaving Rothenburg; you have to change trains there anyway on the way to the Rhine. Stow bags in a locker, see the Residenz Palace and adjacent Hofkirche, and maybe a bit of the old town zone, grab some eats. Leave W'burg around 1 pm for Bingen (takes about 2.5 hours on the fast trains.) Drop bags at hotel (NH Bingen is very conveniently located near train station.) Drop bags at hotel, walk down the river promenade (only a few min.) to the KD boat dock. Take the 16:30 KD cruise of the very best scenery from Bingen to St. Goar (arrive 17:55) if you wish - have a meal, then return by train to Bingen (about 23 min., <€20 total for all 3.) The cruise is €19 adult, €6 for the youngest child cruise, but you get a 20% discount by showing your train ticket at the KD dock.
Don't want to cruise, or want to do it another day? You can visit Bacharach or Oberwesel that afternoon instead. Or take the ferry NOT the cruise boat, but the ferry, which runs all day long) over to Rüdesheim for a look around. Or just relax in Bingen and enjoy the scenery.
WED & THU
There are several outings you can do by train and ferry on these days - Rüdesheim (ferry), Bacharach, Rheinfels Castle in St. Goar, Marksburg Castle in Braubach... maybe you have all this sorted out already. Daytrips by train on a daypass should cost €27/day for the 3 of you - get the Rheinland-Pfalz ticket from a ticket machine.
FRI
Train to FRA. Early morning RE trains are direct and take about 50 min.