Many moons ago, I got a German license without giving up my U.S. license. The Germans wanted to take my U.S. license, but they didn't want to send it to the U.S. or destroy it. They wanted to keep it in a file and have me pay a maintenance fee for the file. I thought that was nuts and was willing to have the license destroyed, but that wasn't an option. The Amt lady suggest I get a letter from the U.S. consulate stating that in the U.S. the license is used much like a Personalausweiss and I would be inconvenienced without it. The U.S. consulate produced such a letter, clearly being familiar with this procedure, and I gave the Amt lady the letter and she gave me a Geman license and let me keep my U.S. license.
don't get a J-1 visa. you will find he is forced to return to Germany for 2 years whether he marries you or not, or has to work for the VA for 3 years, or has to work in an "underserved area" for 3 years (think Northern Exposure).
With a brief Google search I did not find a Stuttgart "Ferienpass", but other cities have them (e.g. Munich and Dresden), check if Stuttgart does. It serves as a summer public transport ticket and as a pass (or discount coupon) to a bunch of kid-friendly activities such as sports, crafts, music, etc.