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In your circumstances I would:
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To check in on your return, you can use either passport. I always check in with my EU passport when flying from the US to the EU, and my US passport when flying from the EU to the US. But the airline doesn't really care one way or the other since US citizens do not need visas in the EU. (I live in the US, however. If you live in the EU, you might need to prove that you are allowed to stay there for more than 90 days before the airline will board you.)
For immigration officials, I always show my EU passport to EU officials and my US passport to US officials.
For non-EU countries other than the US, I pick one or the other. The basic principle then is this:
Each country has one passport associated with it. When traveling to that country, check in with that passport. When showing ID to an official from that country, use that passport.
So far I've never had a situation where I was transiting through a country where I wanted to use one passport but arriving in a country where I wanted to use the other. If I encountered such a situation, I would likely show both passports at checkin.