Just to give a little update on this topic:
Last week Thursday I applied for the so called Exit & Entry permit that allows my boys to leave China and travel to EU/Germany using their German passport.
The application was actually simple and I was able to do the entire task my own as the father, my wife (and mother, who is working in the US) was not required to be present, only her ID-card. All required documents were presented to the officer, including a filled out application form for each of my son, as well the flight booking (e-ticket) with their western/Pinyin names as stated in the German passport.
Tomorrow, June 25th, I can pick up these travel documents, the processing time is only about 3-5 business days, at least here in southern Guangdong. That document is valid for one exit and entry.
Last week Wednesday, I applied for ESTA using the German passport and the was approved within one hour after submission. So also this topic is resolved and let us continue our journey to the US from Germany.
So, this said, everything is resolved and we're all set for our EU/US trip.
When it comes to the next trip to the US, in that case most likely from China directly, I may have a chance using neighboring Hong Kong as an intermediate hop into the US. However, this is a different story and I will come back to report on this as well.
Thanks to the forum and your responses which really shed some light on the topic. Y'all replies were much appreciated help!