If you make it comparable, and ask who could send your nephews to Afghanistan right now, then again - darn near anyone in their chain of command.
For an OPLAN, the document is a TPFDD: Time-Phased Force Deployment Data. It may have a different name under contingency planning, and I don't know which is being used for Afghanistan right now. But the principle remains: the document creates slots, like job openings, if you will. And anyone with the qualifications can be plugged into one of those slots. The document is created under the SecDef's authority, IIRC. That honestly isn't something I had to deal with.
Once created, a commander can put one of their people into it, or is tasked to commit so many people to go. In some cases, and entire squadron would be committed. I had limited experience with TPFDDs, other than in some static forms.
Lots of people could sign the orders - pretty much any commander in the chain. Since Congress funds it, it is authorized by Congress via the military. But no, the President of the USA doesn't sign the orders.
And as long as Obama is accepted by the government as President, he could sign the orders if he wished. The legality of the orders would remain, because he signs them as President, not as an individual. Just as Obamacare would remain a law if Obama was found to be Kenyan-born, so would any military orders he signed (if he could be found to sign them). It is the office that has the authority, not the individual.
In this case:
You said that combat operations were authorized for Afghanistan. Who authorized those? Under the Authorization for the Use of Force that Congress gave in the War on Terror (shortly after 9-11-01), who did Congress say had the sole responsibility to decide when, where, and to what extent force would be used in the war on terror? I don’t believe Afghanistan was specifically mentioned, nor any other country; it was left to one specific person to decide when, where, and to what extent combat would be employed to confront terrorism. What person was that?
IOW, combat in Iran or any other country including Afghanistan WAS authorized, but with the stipulation that combat in any specific place could only happen when one specific person decided there would be combat operations there. What person is that? What one person could - right now - order my nephews in the USMC to board a plane to Iran to engage in combat there? Why can’t anybody else give that order RIGHT NOW?