There are already several questions on this site regarding travel with a minor and only one parent, but I don't think this specific situation has already been covered:
My wife, me, and our minor child live in Germany, but we're currently on vacation in the US (we traveled there together). It turns out that I will be traveling back to Germany alone with our child (my wife will be returning a few days later than us). Our child is a dual US/German citizen. We'll be traveling with Icelandair, changing planes in Iceland (that is, we'll re-enter the Schengen area in Iceland).
Which additional documents do we need for that? So far, we have a parental consent form signed by my wife, and our child's birth certificate (which proves that my wife is indeed the mother). Will that suffice or do we need anything else?