That is the weird exit/entry handling of the Chinese authorities that also includes not recognizing multi-national Chinese citizens. It is what it is. For China, my children are Chinese only, for the remaining (western) world, my children are bi-national.
It is the first time I am doing such a trip CN-> EU -> US -> CN with my kids and additionally I most likely have to apply for an exit/entry permit for them.
This trip in particular may be a bit more easy, cause we first travel to Germany. My kids are German nationals, so they do not get a Schengen visa. Same goes the other way around, for China, no Chinese visa, cause they are also Chinese nationals. Whatssoever, they need to use their German passport to travel to the EU, no matter what.
On the other hand, if we have a direct trip to the US, I have no idea, what kind of rocks the authorities may throw into our way. This is something to find out when that time comes, and it surely will come any time soon, after this summer.
Being Chinese-multi-national ain't a cake-walk, regardless of all pros being in such a position. This is what I also hear from other foreign fellows living/working in China, bi-national families, be it US, EU or whatever constellation.
My apologies I can not give more detailed information at this point. If this topic is of interest in this forum, I am happy to report back. I am not the only parent with multi-national Chinese born children.