You will have plenty of time to do all you want with your diverse group. I would :
* Make a list of what you would like to do and then look at what days certain activities may be free or reduced prices for all of you. Some museums and other places have free days or discounted activities. Look at the options and plan them on those days.
* Remember the weather and have alternatives to outdoor activities that may be impacted by inclement weather.
* Make sure you take a poll and let everyone contribute their ideas on what to do.
* Lastly, do include at least one train travel experience where your teenagers can interact and observe others of their own ages and see how European teens educate themselves on the world.
Good travels on a "Trip of a lifetime" for all!
Legoland Deutchland is a 2-3 hour trip from Frankfurt.
Hamburg is about 4 hours by train and is home to the largest model railroad I've ever seen.
Munich is about 3 hours and has some great museums; their science and technology museum includes a life size salt mine (or was it a coal mine?).
And, there are a bunch of great museums in Frankfurt itself.
Have a fun trip!
You can take a train from Frankfurt to Rudesheim am Rhein. From Rudesheim, take the boat down (which is really heading north... I don't understand it) the Rhine to St. Goar. You will be on the best part of the Rhine and see many, many castles! Also, seeing how they grow grapes on the very steep sides of the river is amazing.
Get off the boat in St. Goar and after strolling around the town (make sure to check out the frescoes in the church), take the little train or walk up to Rheinfels Castle for a tour of the castle, great views of the Rhine and town. Walk back to town and catch a train(s) back to Frankfurt.
Or, Marksburg Castle is another great choice!
Here's a map of castles along the Rhine:
that river rhine trip is really adviseable, but you should indeed also consider going to Hamburg for two days /one night. They have a phantastic Marriott up there in the heart of the city, walking distance to harbour and that minature wonderland train is a dream not only for trainlovers.if you can go on July 31st, they will have the Hamburg Cruise days with 5 or 6 ocean liners parading the harbour.
If you like, contact me any time, I can give you some more tips.
Best regards and wishes from Germany