That’s very good. Use his German passport when going to Germany of course, or any other 3rd country. One time I had mixed up and gave my child Taiwanese passport to the immigration office in the UK and he started asking a bunch of questions, then I looked over and saw I had given him the wrong passport. Then I handed him the other passport my child has. He saw we had both same family names. He didn’t ask anything else and just stamped our passports and welcomed us. I have since travelled many times to may countries alone with only her and nothing else happened.
First time I took my child abroad with me alone she was just a little older than 2.
We travelled dozen of times to many different countries each time and no one ever asked anything expect the situation above in the UK. I always used her non Taiwanese passport though, out of Taiwan. I am a holder of APRC so don’t know if that helps when I leave and come back to taiwan because no officer has ever asked about any approval document from the other parent.
Just for fun fact, I always used the ‘Permanent Residents Only’ line at Taiwan immigration. Even though she is Taiwanese I always took her to APRC,ARC holders line and the officers seem faster with their time checking stuff. Remember if you have the e-gate you won’t be able to use it because you are will be with your child.
I might be bluffing but I always though the reason for not being asked a single time in over dozens of trips alone with a little kid is that the officers in the Permanent Residents only line are checking so many foreigners that day that is not an uncommon thing. I imagined if you are checkin thousands of Taiwanese people on that day and then suddenly see a foreigner with a little one trying to leave thy would be asking more questions and causing problems.
If you want peace of mind you can have a letter of consent (try to see if there is any standard format online) and then have is signed/stamped by the other parent with a pubic notary stamp. That would be the maximum already. If you want you can take the Household membership but that wouldn’t need to be notarized since you are presenting it to a Taiwanese government personal. I really don’t think they will ask anything. But better safe than sorry.
Does the German passport have the parents name in a secondary page? Not the page with the picture.