Yes, because Romania is not part of the Schengen area, you must go through passport control at both Germany and Romania. However, as long as you use your Romania passport you should be fine, as Germany will admit you solely on that. They should not care what's on your ticket. They should not even need you to show your ongoing ticket.

Ultimately, the green card is not really a travel document and is an internal US government document. As such, it is only acceptable in the US as a form of ID. You should ticket in your passport name when going overseas as foreign authorities will likely only treat a passport as the "true" ID.

As TrueBlueFlyer mentioned, I would also check with someone knowledgeable to make sure she does not require some sort of "reentry permit" to come back into the US. I have zero experience in this area but I imagine it would be really annoying to be stuck outside the US and unable to enter because of some bureaucratic snafu at the USCIS - although your wife might enjoy more time in Romania.

BTW I will also bring your copy of the marriage certificate just in case. It probably won't be needed but sometimes you are just lucky enough get the dumbest agent at immigration...