Based on your interests there have been some good recommendations
--Skipping Frankfurt / Mainz for Hamburg could work, but of course so does going to Frankfurt and Mainz. I, of course, favour Hamburg. The two cities are very different. They have more Ancient / Medieval history, we have more Renaissance and maritime history. Think half-timbered houses and Roman ruins vs. pirates and Vikings and international shipping. Both cities are worth a visit.
--Don't get a car for Mainz. Get it to leave Mainz.
--Not sure how you chose Trendelburg, but the drive from Frankfurt / Mainz to Bremen is probably not going to take you near there. It would, however, take you along the Rhine, a gorgeous drive in and of itself, past Koblenz (take an hour to visit the Deutsches Eck), past Cologne (take two hours to visit the cathedral--seriously, it is WELL worth the visit) and then up the A1 past Münster. If it's just about breaking up the drive, I would actually spend the night in Köln--an easy day from Mainz to Köln, hit the cathedral in the evening, and an easy day from Köln to Bremen. The first day is only about a 3 hour drive along the Rhine (shorter if you go highway, but why?), but of course with lots of gorgeous stops of your choosing or possible side trips. The Lorelei would be a cultural point as well, so it might interest your son. I would also try to hit St. Ursula and its bone crypt in Köln. From Köln to Bremen is about 4 hours by car, and it is absolutely boring (well, you go through Münster, but given your interests it probably isn't worth it).
--If you are planning the A7 route, you should know that this road is equally hateful in the summer. It's a 5 hour drive to Bremen from Frankfurt, but it is not a fun one. Okay, full disclosure, I hate the A7 between Hannover and Kassel with a fiery passion. But if you prefer to go this route, I would only break it up if necessary. Alternatively, a train might be a more interesting way to go. It is only 4 hours from Frankfurt to Bremen by train, so it's faster, you don't have to drive the A7 through Kassel / Göttingen, and you save a day. It's a very local thing to take the ICE. You could also save on the rental car for another day or two, which easily pays for the train tickets.
--2 nights in Bremen. I ADORE this city, but it isn't big or sprawling. You can easily see it in a full day, certainly in 1,5 days.
Now you are in for a treat--the German north in the summer. If you skip the extra travel time and only do two nights in Bremen, you could hit a few local hubs, some smaller, some larger:
Places you may not have considered include:
--Emden / Aurich / Greetsiel (a true hidden gem! Seriously!):
**The East Frisian Tea Ceremony is a UNESCO cultural heritage event
--Glückstadt:
**Northern Germany's Danish past, the 30 Years War, religious diversity, a harbour that looks like Copenhagen's Nyhavn, and a unique street layout make this adorable town worth visiting.
--St. Peter-Ording:
**Wadden Sea UNESCO site can be toured with local guides--in German, absolutely stunning, and a truly local experience
--Helgoland:
**Spend the night, visit the bunker, see the red cliffs, learn about the local language spoken only here, and see the seals on the beach (or even swim with them if they choose to come into the human area).
Okay, for the next part of your itinerary, suggestions include Haithabu, Plön, and Bad Segeberg as places to see from Lübeck, which is amazing.
And I will let Mignon talk about Stralsund, Rügen, and the MeckPomm part of the trip.
For the return to Frankfurt, ditch Magdeburg in favour of Wernigerode. You will not be sorry! If you have time, an extra night in the Harz is worth it. And that route takes you through the Elbtalaue, IMO one of the prettiest places in Germany (Dömnitz area).
If you saw Frankfurt on the way in, one night is all you need--get in, have some dinner, sleep, fly out.
