With boys your age this is a great region! I don't think a lot of the advice here is geared towards kids. I generally am a fan of trains but exploring Bavaria/Austria by car makes more sense generally and will save you some money, too.
To experience a high speed rail ride, I'd take the ICE train from Frankfurt Airport directly to Munich, that would be a fun experience and it will save you trying to drive while jetlagged, and shaves about an hour off the driving time. Plus you won't need a car in Munich.
I'd spend 4 nights in Munich, there's a ton to see and do. Even if you're not museum people, the Deutches Museum is a science and technology museum that's a must for kids and adults. I'd visit the Hofbrauhaus for the atmosphere, but there are better (and cheaper) places to eat. Definitely watch the "surfers" on the Isar then walk through the Englisher garten to the Chinesicher Turm biergarten. Another great Biergarten worth visiting is the Augustiner Biergarten near the HBF. Food prices at biergartens are cheap and the portions are hearty. And keep in mind that large biergartens often have playgrounds so they're a great place for kids to blow off steam while mom and dad relax with a beer. Take a tour of one of the palaces in the city, that's totally worth it (I like the Residenz, personally). Shop for cheese and salami and produce at the Vituaklienmarkt. Check out the nearby Heilig-Geist-Kirche (Holy Ghost Church) for some creepy relics in the form of a skeleton of a saint, all blinged out. Popping your head into churches in Bavaria you're likely to see a lot of relics.
From there you could easier stay in Munich a few more days using it as a base to see nearby cities via train (Regensburg, Bamberg, and Nurnberg are all worth visiting, in that order) or you could rent a car and head for Fussen for the castles (Neuschwanstein and Hohenschwangau). Don't let people here tell you they're not worth seeing, I've seen a buttload of German Castles and none has a setting as breathtaking as Neuschwanstein, and it's still "historic" by American standards, as historic as the Winchester Mansion or Hearst Castle, anyway!
From there I'd drive to Berchesgadenerland. Basing in Salzburg makes sense, but Berchdesgaden gives you that German alpine village feel (albeit yes, with plenty of tourists. This area is popular for a reason!) You could easily spend 4 nights there, visiting the Eagle's Nest, the Koeningsee (take the boat, it's well worth it!), hiking, visiting villages in the area, salt mines, Sound of Music tour (do it, everyone has fun on it!)
I'd drive over and spend one night in Halstatt, there's not a ton to "see" but the setting is so stunning that I really think it's worth it. Yes, expect more tourists.
After that you've got a few more days, and you're flying out of Frankfurt, so if you're willing to pay extra to drop off your car in another city, doing a bit of the Romantic Road makes perfect sense to me. Don't stay in Rothenburg ob der Tauber, it's touristy AND overrated given how stunning the other towns on the Road are. I'm a big fan of Noerdlingen, but if you want to be closer to Rothenberg for the Night Watchman's tour (this you should do) Dinkelsbuhl is another good option. There are some great nearby villages that aren't on the Romanatic Road proper that are worth visiting, like Swabisch Hall, or Aalen for their ruins of a Roman fortress.
If you let us know when you're visiting we can recommend if any festivals are going on. Germans have festivals from May-October, basically, so there's always something going on.