You have several issues:
1. A Green Card is for living in the US. You must have domicile or intent to re-establish domicile in the US as her petitioner.
2. She can't DCF in Germany since she resides elsewhere.
3. She can't DCF in her country since you reside elsewhere.
4. What you posted does not appear, imho, to be an exceptional circumstance. Separation is normal for US immigration.